Section 2.3.0 - Introductory Writeups
Section 2.3.0.1 - Basic Writeups
Section 2.3.0.1.1 - Part 1 - Katariya - Introduction to Algebra
Section 2.3.0.1.2 - Part 2 - Wikipedia - List of Linear Algebra topics
Section 2.3.0.1.3 - Part 3 - Wikipedia - Matrices
Section 2.3.0.1.3 - Part 4 - Wikipedia - List of Matrices
Section 2.3.0.1.5 - Part 5 - DeepLearningOrg - Linear Algebra for Deep Learning
Section 2.3.0.1.6 - Part 6 - Wikibooks - Linear Algebra
Section 2.3.0.1.7 - Part 7 - Robert A Beezer - A first course in Linear Algebra
Section 2.3.0.1.8 - Part 8 - Wikipedia - Algebra Portal
Section 2.3.0.2 - Detailed Writeups
Section 2.3.0.2.1 - Part 1 - Cherney,Denton,Thomas,Waldron - Linear Algebra
Section 2.3.0.2.2 - Part 2 - Dawkins - Linear Algebra
Section 2.3.0.2.3 - Part 3 - Carrell - Fundamentals of Linear Algebra
Section 2.3.0.2.4 - Part 4 - Lipschutz-Lipson - Schaum's Linear Algebra
Section 2.3.0.2.5 - Part 5 - Lang - Introduction to Linear Algebra
Section 2.3.0.2.6 - Part 6 - Strang 4rth Edition - Linear Algebra and its applications
Section 2.3.0.2.7 - Part 7 - Hoffman,Kunze - Linear Algebra
Section 2.3.0.3 - Videos
Section 2.3.0.3.1 - Part 1 - 3Blue1Brown - Essence of Linear Algebra
Section 2.3.0.3.2 - Part 2 - MIT - Gilbert Linear Albegra Course by Gilbert Strang
Section 2.3.0.3.3 - Part 3 - Imperial College London - Linear Albegra for Machine Learning
Section 2.3.0.3.4 - Part 4 - Imperial College London - Linear Albegra for Machine Learning
Section 2.3.0.3.5 - Part 5 - Khan Academy - Linear Algebra
Section 2.3.0.3.6 - Part 6 - Khan Academy - Linear Algebra
Section 2.3.0.3.7 - Part 7 - Racheal Thomas - Computational Linear Algebra
Section 2.3.1 - Basic Concepts
Section 2.3.1.1 - Numerical Linear Algebra
Section 2.3.1.2 - Fundamental Theorem of Algebra
Section 2.3.1.3 - Fundamental Theorem of Linear Algebra
Section 2.3.1.4 - Scalar
Section 2.3.1.5 - Scalar Multiplication
Section 2.3.1.6 - Vector Space
Section 2.3.1.7 - Vector Projection
Section 2.3.1.8 - Linear Map
Section 2.3.1.9 - Linear Projection
Section 2.3.1.10 - Basis
Section 2.3.1.11 - Change of Basis
Section 2.3.1.12 - Matrices
Section 2.3.1.13 - Row And Column Space
Section 2.3.1.14 - Orthogonality
Section 2.3.1.15 - Determinant
Section 2.3.1.16 - Eigenvalues and Eigenvectors
Section 2.3.1.17 - Duality
Section 2.3.1.17.0 - Basic Writeup - Wikipedia - Duality
Section 2.3.1.17.1 - Dual Map
Section 2.3.1.17.2 - Inner Product Space
Section 2.3.1.18 - Linear Algebra Machine Learning Examples
Section 2.3.1.18.1 - Linear Regression
Section 2.3.1.18.2 - Regularization
Section 2.3.1.18.3 - Principal Component Analysis
Section 2.3.1.18.4 - One Hot Encoding
Section 2.3.1.18.5 - Latent Semantic Analysis
Section 2.3.1.18.6 - Recommender System
Section 2.3.1.18.7 - Deep Learning
Section 2.3.2 - Vectors and Vector spaces
Section 2.3.2.0 - Basic Writeup - Wikipedia - Vector
Section 2.3.2.1 - Vector Algebra
Section 2.3.2.1.0 - Basic Writeup - UNL - Vector Algebra
Section 2.3.2.1.1 - Scalar multiplication
Section 2.3.2.1.2 - Vector Dot Product
Section 2.3.2.1.3 - Vector Dot Product
Section 2.3.2.1.4 - Bilinear Map
Section 2.3.2.1.4.0 - Basic Writeup - Wikipedia - Bilinear Map
Section 2.3.2.1.4.1 - Cross product
Section 2.3.2.1.4.2 - Triple product
Section 2.3.2.1.4.3 - Seven-dimensional Cross Product
Section 2.3.2.2 - Specific Vector Types
Section 2.3.2.2.1 - Zero Vector
Section 2.3.2.2.2 - Basis Vector
Section 2.3.2.2.3 - Unit Vector
Section 2.3.2.2.4 - Isotropic(Null) Vector
Section 2.3.2.2.5 - Column Vector
Section 2.3.2.2.6 - Row and Column Vector
Section 2.3.2.2.7 - Coordinate Vector
Section 2.3.2.2.8 - PseudoVector
Section 2.3.2.2.9 - Tangent Vector
Section 2.3.2.2.10 - Normal Vector
Section 2.3.2.2.11 - Gradient Vector
Section 2.3.2.2.12 - More Categories of Vectors
Section 2.3.2.3 - Vector Norms
Section 2.3.2.3.0 - Basic Writeup - Wikipedia - Vector Norms
Section 2.3.2.3.1 - Distance Metrics
Section 2.3.2.3.1.1 - Euclidean (Pythagorean) Distance
Section 2.3.2.3.1.2 - Chebyshev Distance
Section 2.3.2.3.1.3 - Manhattan (Rectilinear,L1,Snake,City Block) Distance
Section 2.3.2.3.1.4 - Minkowski Distance
Section 2.3.2.3.1.5 - Haversine Distance
Section 2.3.2.3.2 - Vector L1 Norm (Taxicab Metric - Taxicab Geometry)
Section 2.3.2.3.3 - Vector L2 (Euclidean) Norm
Section 2.3.2.3.1.4 - Vector Max(Infinity/Uniform/Supremum) Norm
Section 2.3.2.4 - Vector Products
Section 2.3.2.4.1 - Outer Product
Section 2.3.2.4.2 - Inner Product Space
Section 2.3.2.4.3 - Dot Product
Section 2.3.2.4.4 - Cross Product
Section 2.3.2.4.5 - Direct Product
Section 2.3.2.4.6 - Triple Product (Scalar and Vector)
Section 2.3.2.5 - Vector Space
Section 2.3.2.5.0 - Basic Writeups
Section 2.3.2.5.0.1 - Part 1 - Wikipedia - Vector Space
Section 2.3.2.5.0.2 - Part 2 - Wikibooks - Definitions and Examples
Section 2.3.2.5.0.3 - Part 3 - Wikipedia - More Examples of Vector Spaces
Section 2.3.2.5.0.4 - Part 4 - Wikipedia - Categories of Vector Spaces
Section 2.3.2.5.1 - Subspace and Spanning Sets
Section 2.3.2.5.2 - Dual Space
Section 2.3.2.5.2.0 - Basic Writeup - Wikipedia - Dual Space
Section 2.3.2.5.2.1 - Linear Function
Section 2.3.2.5.2.2 - Linear Functional
Section 2.3.2.5.2.3 - Algebraic Dual Space
Section 2.3.2.5.2.4 - Continuous Dual Space
Section 2.3.2.5.3 - Linear Subspace
Section 2.3.2.5.3.0 - Basic Writeup - Wikipedia - Linear Subspace
Section 2.3.2.5.3.1 - Row and Column Spaces
Section 2.3.2.5.3.2 - Cyclic Subspace
Section 2.3.2.5.3.3 - Null(Kernel) Space
Section 2.3.2.5.4 - Linear Span
Section 2.3.2.5.5 - Basis (Linear Algebra)
Section 2.3.2.5.6 - Quotient Vector Space
Section 2.3.2.5.7 - Normed Vector Space
Section 2.3.2.5.8 - Graded Vector Space
Section 2.3.2.5.9 - Ordered Vector Space
Section 2.3.2.5.10 - Super Vector Space
Section 2.3.2.5.11 - Topological Vector Space
Section 2.3.2.5.11.0 - Basic Writeup - Wikipedia - Topololigical Vector Space
Section 2.3.2.5.11.1 - F-Spaces
Section 2.3.2.5.11.2 - Locally Convex
Section 2.3.2.5.11.2.0 - Basic Writeup - Wikipedia - Locally Convex
Section 2.3.2.5.11.2.1 - Barrelled Spaces
Section 2.3.2.5.11.2.1.0 - Basic Writeup - Wikipedia - Barrelled Spaces
Section 2.3.2.5.11.2.1.1 - Montel Space
Section 2.3.2.5.11.2.2 - Bornological Spaces
Section 2.3.2.5.11.2.3 - Stereotype Space
Section 2.3.2.5.11.2.4 - Fréchet spaces
Section 2.3.2.5.11.2.4.0 - Basic Writeup - Wikipedia - Fréchet spaces
Section 2.3.2.5.11.2.4.1 - Fréchet Algebra
Section 2.3.2.5.11.2.4.2 - LF-spaces
Section 2.3.2.5.11.2.5 - Nuclear spaces
Section 2.3.2.5.11.2.6 - Normed Spaces
Section 2.3.2.5.11.2.6.0 - Basic Writeup - Wikipedia - Normed Spaces
Section 2.3.2.5.11.2.6.1 - Banach Spaces
Section 2.3.2.5.11.2.6.1.0 - Basic Writeup - Wikipedia - Banach Spaces
Section 2.3.2.5.11.2.6.1.1 - Banach Algebra
Section 2.3.2.5.11.2.6.1.1.0 - Basic Writeup - Wikipedia - Banach Algebra
Section 2.3.2.5.11.2.6.1.1.1 - C*-Algebra
Section 2.3.2.5.11.2.6.1.1.1.0 - Basic Writeup - Wikipedia - C*-Algebra
Section 2.3.2.5.11.2.6.1.1.1.1 - Von Neumann Algebra
Section 2.3.2.5.11.2.6.2 - Hardy paces
Section 2.3.2.5.11.2.6.3 - Hilbert Spaces
Section 2.3.2.5.11.2.7 - Semi-Normed Spaces
Section 2.3.2.5.11.2.8 - Sobolov Spaces
Section 2.3.2.5.12 - Symplectic Vector Space
Section 2.3.2.5.13 - Algebra Over Fields
Section 2.3.2.5.14 - Lie Algebra
Section 2.3.2.5.15 - Dimension Theorem For Vector Spaces
Section 2.3.2.5.15.0 - Basic Writeup - Wikipedia - Dimension Theorem For Vector Spaces
Section 2.3.2.5.15.1 - Hamel Dimension
Section 2.3.2.6 - Maps Between Spaces
Section 2.3.2.6.1 - Linear map (transformation, linear function)
Section 2.3.2.6.1.0 - Basic Writeup - Wikipedia - Linear map (transformation, linear function)
Section 2.3.2.6.1.1 - Geometry of Linear Maps
Section 2.3.2.6.1.2 - The Matrix of a Linear Map
Section 2.3.2.6.1.3 - Discontinuous Linear Maps
Section 2.3.2.6.1.4 - Projections of Linear Maps
Section 2.3.2.6.1.4.0 - Basic Writeup - Wikipedia - Projections of Linear Maps
Section 2.3.2.6.1.4.1 - Projection Onto a Subspace
Section 2.3.2.6.1.4.2 - Vector Projection
Section 2.3.2.6.1.4.2.0 - Basic Writeup - Wikipedia - Vector Projection
Section 2.3.2.6.1.4.2.1 - Orthogonal Projection
Section 2.3.2.6.1.4.2.2 - Orthogonal Projection Onto a Line
Section 2.3.2.6.1.4.2.3 - Parallel Projection
Section 2.3.2.6.1.4.3 - Gram-Schmidt Orthogonalization
Section 2.3.2.6.2 - Shear mapping or Galilean transformation
Section 2.3.2.6.3 - Squeeze mapping or Lorentz transformation
Section 2.3.2.6.4 - Tranformation Matrix
Section 2.3.2.6.6 - Kernel
Section 2.3.2.6.7 - Cokernel
Section 2.3.2.6.8 - Algebraic Classifications
Section 2.3.2.6.8.1 - Epimorphism (Surjective)
Section 2.3.2.6.8.2 - Isomorphism
Section 2.3.2.6.8.2.0 - Basic Definition - Wikipedia - Isomorphism
Section 2.3.2.6.8.2.1 - Definition and Examples
Section 2.3.2.6.8.2.2 - Dimension Characterizes Isomorphism
Section 2.3.2.6.8.3 - Endomorphism
Section 2.3.2.6.8.3.0 - Basic Writeup - Wikipedia - Endomorphism
Section 2.3.2.6.8.3.1 - Eigenvalue, eigenvector and eigenspace
Section 2.3.2.6.8.3.1.0 - Basic Writeup - Wikipedia - Eigenvalue, eigenvector and eigenspace
Section 2.3.2.6.8.3.1.1 - Cayley–Hamilton theorem
Section 2.3.2.6.8.3.1.2 - Spread of a matrix
Section 2.3.2.6.8.3.1.3 - Jordan normal form
Section 2.3.2.6.8.3.1.4 - Weyr canonical form
Section 2.3.2.6.8.3.1.5 - Eigenvectors from Eigenvalues
Section 2.3.2.6.8.4 - Homomorphisms
Section 2.3.2.6.8.4.0 - Basic Writeup - Wikipedia - Homomorphisms
Section 2.3.2.6.8.4.1 - Rangespace and Nullspace
Section 2.3.2.6.8.4.2 - Monomorphism (Injective homomorphism)
Section 2.3.2.6.9 - Computing Linear Maps
Section 2.3.2.6.9.0 - Basic Writeup - Wikipedia - Computing Linear Maps
Section 2.3.2.6.9.1 - Representing Linear Maps with Matrices
Section 2.3.2.6.9.2 - Any Matrix Represents a Linear Map
Section 2.3.2.6.10 - Basis
Section 2.3.2.6.10.0 - Basic Writeup - Wikipedia - Basis
Section 2.3.2.6.10.1 - Subspaces
Section 2.3.2.6.10.2 - Quotient Spaces
Section 2.3.2.6.10.3 - Direct product
Section 2.3.2.6.10.4 - Direct Sum (Of Groups)
Section 2.3.2.6.10.5 - Tensor Product
Section 2.3.2.6.10.6 - Change of Basis
Section 2.3.2.6.10.6.0 - Basic Writeup - Wikipedia - Change of Basis
Section 2.3.2.6.10.6.1 - Changing Representations of Vectors
Section 2.3.2.6.10.6.2 - Changing Map Representations
Section 2.3.2.6.10.7 - Hamel Basis
Section 2.3.2.6.11 - Line of Best Fit
Section 2.3.2.6.12 - Markov Chains
Section 2.3.2.6.13 - Orthonormal Matrices
Section 2.3.3 - Systems of Linear Equations
Section 2.3.3.0 - Basic Writeup - Wikipedia - Systems of Linear Equations
Section 2.3.3.1 - Linear Equations
Section 2.3.3.1.0 - Basic Writeup - Wikipedia - Linear Equations
Section 2.3.3.1.1 - Determinant
Section 2.3.3.1.2 - Minor(Linear Algebra)
Section 2.3.3.1.3 - Cauchy–Binet formula
Section 2.3.3.1.4 - Cramer's rule
Section 2.3.3.1.5 - Gaussian(Gauss-Jordan) Elimination
Section 2.3.3.1.6 - Strassen algorithm
Section 2.3.3.2 - Solving Linear Systems of Equations (See Section 2.3.10.2 for detailed breakdown in Numerical Linear Algebra)
Section 2.3.3.3 - Linear Geometry of n-Space
Section 2.3.3.3.0 - Basic Writeup - Wikibooks - Linear Geometry of n-Space
Section 2.3.3.3.1 - Vectors in Space
Section 2.3.3.3.2 - Length and Angle Measures
Section 2.3.3.4 - Reduced Echelon Form
Section 2.3.3.4.0 - Basic Writeup - Wikibooks - Reduced Echelon Form
Section 2.3.3.4.1 - Gauss-Jordan Reduction
Section 2.3.3.4.2 - Row Equivalence
Section 2.3.3.5 - Computer Algebra Systems
Section 2.3.3.6 - Input-Output Analysis
Section 2.3.3.7 - Accuracy of Computations
Section 2.3.3.8 - Analyzing Networks
Section 2.3.3.9 - Speed of Gauss' Method
Section 2.3.3.10 - Linear span
Section 2.3.3.11 - Linear independence
Section 2.3.3.12 - Linear combination
Section 2.3.4 - Similarity
Section 2.3.4.0 - Basic Writeup - Wikibooks - Similarity
Section 2.3.4.1 - Definition and Examples
Section 2.3.4.2 - Diagonalizability
Section 2.3.4.3 - Eigenvalues and Eigenvectors
Section 2.3.4.4 - Complex Vector Spaces
Section 2.3.4.4.0 - Basic Writeup - Wikibooks - Complex Vector Spaces
Section 2.3.4.4.1 - Factoring and Complex Numbers: A Review
Section 2.3.4.4.2 - Complex Representations
Section 2.3.4.5 - Nilpotence
Section 2.3.4.5.0 - Basic Writeup - Wikibooks - Nilpotence
Section 2.3.4.5.1 - Self-Composition
Section 2.3.4.5.2 - Strings
Section 2.3.4.6 - Jordan Form
Section 2.3.4.6.0 - Basic Writeup - Wikibooks - Jordan Form
Section 2.3.4.6.1 - Polynomials of Maps and Matrices
Section 2.3.4.6.2 - Jordan Canonical Form
Section 2.3.4.7 - Geometry of Eigenvalues
Section 2.3.4.8 - The Method of Powers
Section 2.3.4.9 - Stable Populations
Section 2.3.4.10 - Linear Recurrences
Section 2.3.5 - Matrices
Section 2.3.5.0 - Basic Writeup - Wikipedia - Matrices
Section 2.3.5.1 - Matrix Operations
Section 2.3.5.1.1 - Matrix addition
Section 2.3.5.1.2 - Matrix multiplication
Section 2.3.5.1.2.0 - Basic Writeup - Wikipedia - Matrix multiplication
Section 2.3.5.1.2.1 - Mechanics of Matrix Multiplication
Section 2.3.5.1.2.2 - Algorithms for matrix multiplication:
Section 2.3.5.1.2.2.1 - Strassen algorithm
Section 2.3.5.1.2.2.2 - Coppersmith–Winograd algorithm
Section 2.3.5.1.2.2.3 - Cannon's algorithm
Section 2.3.5.1.2.2.4 - Freivalds' algorithm
Section 2.3.5.1.3 - Matrix Norms
Section 2.3.5.1.4 - Matrix Splitting
Section 2.3.5.1.5 - Basis transformation matrix
Section 2.3.5.1.6 - Sums and Scalar Products
Section 2.3.5.1.7 - Invertable Matrix
Section 2.3.5.1.8 - Pseudoinverse
Section 2.3.5.1.9 - Transpose
Section 2.3.5.1.9.0 - Basic Writeup - Wikipedia - Transpose
Section 2.3.5.1.9.1 - Symmetric matrix ( A = AT )
Section 2.3.5.1.9.2 - Orthogonal matrix ( AT = A-1 )
Section 2.3.5.1.9.3 - Skew-symmetric matrix ( AT = -A )
Section 2.3.5.1.9.4 - Conjugate Transpose matrix
Section 2.3.5.1.9.4.0 - Basic Writeup - Wikipedia - Conjugate Transpose matrix
Section 2.3.5.1.9.4.1 - Unitary matrix
Section 2.3.5.1.9.4.2 - Hermitian matrix
Section 2.3.5.1.9.4.3 - Skew-Hermitian (Antihermitian) matrix
Section 2.3.5.1.10 - Rank
Section 2.3.5.1.11 - Square Matrix
Section 2.3.5.1.11.0 - Basic Writeup - Wikipedia - Square Matrix
Section 2.3.5.1.11.1 - Trace
Section 2.3.5.1.11.2 - Determinant
Section 2.3.5.1.11.2.0 - Basic Writeup - Wikipedia - Determinant
Section 2.3.5.1.11.2.1 - Determinants as Size Functions
Section 2.3.5.1.11.2.2 - Laplace's Expansion
Section 2.3.5.1.11.2.3 - Cramer's Rule
Section 2.3.5.1.11.2.4 - Speed of Calculating Determinants
Section 2.3.5.1.11.2.5 - Projective Geometry
Section 2.3.5.1.11.3 - Characteristic polynomial
Section 2.3.5.1.11.4 - Cofactor
Section 2.3.5.1.11.5 - Adjugate
Section 2.3.5.1.11.6 - Pfaffian
Section 2.3.5.1.11.7 - Minor
Section 2.3.5.2 - Row and column spaces
Section 2.3.5.3 - Spectral theorem
Section 2.3.5.4 - Perron–Frobenius theorem
Section 2.3.5.5 - Types of Matrix
Section 2.3.5.5.1 - Square Matrix and Types
Section 2.3.5.5.1.0 - Basic Writeup - Wikipedia - Square Matrix
Section 2.3.5.5.1.1 - Diagonal Matrix
Section 2.3.5.5.1.2 - Triangular Matrix
Section 2.3.5.5.1.3 - Identity Matrix
Section 2.3.5.5.1.4 - Orthogonal Matrix
Section 2.3.5.5.1.5 - Symmetric Matrix
Section 2.3.5.5.1.5.0 - Basic Writeup - Wikipedia - Symmetric Matrix
Section 2.3.5.5.1.5.1 - Hessian Matrix
Section 2.3.5.5.1.5.2 - Antimetric Matrix
Section 2.3.5.5.1.5.3 - Centrosymmetric Matrix
Section 2.3.5.5.1.5.4 - Circulant Matrix
Section 2.3.5.5.1.5.5 - Covariance Matrix
Section 2.3.5.5.1.5.6 - Coxeter Matrix
Section 2.3.5.5.1.5.7 - Hankel Matrix
Section 2.3.5.5.1.5.8 - Hilbert Matrix
Section 2.3.5.5.1.5.9 - Persymmetric Matrix
Section 2.3.5.5.1.5.10 - Skew-symmetric Matrix
Section 2.3.5.5.1.5.11 - Toeplitz Matrix
Section 2.3.5.5.1.5.12 - Hessenberg Matrix
Section 2.3.5.5.1.5.13 - Stochastic Matrix
Section 2.3.5.5.1.5.14 - Hankel Matrix
Section 2.3.5.5.1.6 - Unitary Matrix
Section 2.3.5.5.1.7 - Hermitian Matrix
Section 2.3.5.5.1.8 - Skew(Anti) Hermitian Matrix
Section 2.3.5.5.1.9 - Positive-definite and Semi-Definite Matrix
Section 2.3.5.5.2 - Band Matrix
Section 2.3.5.5.2.0 - Basic Writeup - Wikipedia - Band Matrix
Section 2.3.5.5.2.1 - Tridiagonal Matrix
Section 2.3.5.5.3 - Block Matrix
Section 2.3.5.5.4 - Sparse Matrix
Section 2.3.5.5.5 - Vandermonde Matrix
Section 2.3.5.5.6 - Logical (0,1) Matrix
Section 2.3.5.5.7 - Sparse Matrix
Section 2.3.5.6 - Some useful matrix identities
Section 2.3.5.6.1 - Matrix-vector product as linear combination of matrix columns
Section 2.3.5.6.2 - Sum of outer products as matrix-matrix product
Section 2.3.5.6.3 - Quadratic forms
Section 2.3.5.7 - Decomposition (Factorization)
Section 2.3.5.7.0 - Decomposition (Factorization)
Section 2.3.5.7.1 - Matrix Decomposition
Section 2.3.5.7.1.0 - Basic Writeup - Wikipedia - Matrix Decomposition
Section 2.3.5.7.1.1 - Decompositions Related to Solving Systems of Linear Equations
Section 2.3.5.7.1.1.1 - LU Decomposition
Section 2.3.5.7.1.1.2 - LU Reduction
Section 2.3.5.7.1.1.3 - Block LU Reduction
Section 2.3.5.7.1.1.4 - Rank Factorization
Section 2.3.5.7.1.1.5 - Cholesky Decomp
Section 2.3.5.7.1.1.6 - QR Decomp
Section 2.3.5.7.1.1.7 - RRQR Decomp
Section 2.3.5.7.1.1.8 - Interpolative Decomp
Section 2.3.5.7.1.1.8 - Crout matrix decomposition
Section 2.3.5.7.1.2 - Decompositions Related to Eigenvalues and Related Concepts
Section 2.3.5.7.1.2.1 - Eigen Decomp
Section 2.3.5.7.1.2.2 - Jordan-Chevalley Decomp
Section 2.3.5.7.1.2.3 - Schur Decomp
Section 2.3.5.7.1.2.4 - Real Schur Decomp
Section 2.3.5.7.1.2.5 - Takagi's Factorization
Section 2.3.5.7.1.2.6 - QZ Decomp
Section 2.3.5.7.1.2.7 - Singular Value Decomp
Section 2.3.5.7.1.2.8 - Scale Invariant Decompositions
Section 2.3.5.7.1.3 - Other Decomposition Techniques
Section 2.3.5.7.1.3.1 - Polar Decomposition
Section 2.3.5.7.1.3.2 - Algebraic Polar Decomposition
Section 2.3.5.7.1.3.3 - Mostow's decomposition
Section 2.3.5.7.1.3.4 - Sinkhorn normal form
Section 2.3.5.7.1.3.5 - Sectoral decomposition
Section 2.3.5.7.1.3.6 - Williamson's normal form
Section 2.3.6 - Structures
Section 2.3.6.1 - Nullspace, range
Section 2.3.6.2 - Metric spaces
Section 2.3.6.3 - Normed spaces
Section 2.3.6.4 - Semi-Normed spaces
Section 2.3.6.5 - Inner product spaces
Section 2.3.6.5.0 - Basic Writeup - Wikipedia - Inner product spaces
Section 2.3.6.5.1 - Cauchy-Schwarz inequality
Section 2.3.6.5.2 - Orthogonality
Section 2.3.6.5.3 - Orthogonal complement
Section 2.3.6.5.4 - Orthogonal projection
Section 2.3.6.5.5 - Orthogonal group
Section 2.3.6.6 - Eigen Spaces
Section 2.3.6.7 - Topological vector space
Section 2.3.6.8 - Pseudo-Euclidean space
Section 2.3.6.8.0 - Basic Writeup - Wikipedia - Pseudo-Euclidean space
Section 2.3.6.8.1 - Null vector
Section 2.3.6.8.2 - Indefinite orthogonal group
Section 2.3.6.9 - Orientation (geometry)
Section 2.3.6.9.0 - Basic Writeup - Wikipedia - Orientation (geometry)
Section 2.3.6.9.1 - Improper rotation
Section 2.3.6.10 - Symplectic structure
Section 2.3.7 - Multi-Linear Algebra
Section 2.3.7.0 - Basic Writeup - Wikipedia - Multi-Linear Algebra
Section 2.3.7.1 - p-Vectors and Multivectors
Section 2.3.7.2 - Multilinear Map
Section 2.3.7.2.0 - Basic Writeup - Wikipedia - Multilinear Map
Section 2.3.7.2.1 - Bilinear Map
Section 2.3.7.2.2 - Bilinear Operators
Section 2.3.7.2.3 - Multilinear Form
Section 2.3.7.2.4 - Multilinear Subspace Learning
Section 2.3.7.3 - Exterior Algebra
Section 2.3.7.4 - Exterior Algebra
Section 2.3.7.5 - Exterior Derivative
Section 2.3.7.6 - Tensors
Section 2.3.7.6.0 - Basic Writeup - Wikipedia - Tensors
Section 2.3.7.6.1 - Classical treatment of Tensors
Section 2.3.7.6.2 - Component-free treatment of tensors
Section 2.3.7.6.3 - Mathematical Scope of Tensors
Section 2.3.7.6.3.1 - Coordinate System
Section 2.3.7.6.3.2 - Multilinear Algebra
Section 2.3.7.6.3.3 - Euclidean Geometry
Section 2.3.7.6.3.4 - Tensor Algebra
Section 2.3.7.6.3.5 - Dyadic Algebra
Section 2.3.7.6.3.6 - Dyadic Algebra
Section 2.3.7.6.3.7 - Differential Geometry
Section 2.3.7.6.3.8 - Exterior Calculus
Section 2.3.7.6.3.9 - Tensor Calculus
Section 2.3.7.6.4 - Tensor Notation
Section 2.3.7.6.4.1 - Index Notation
Section 2.3.7.6.4.2 - Multi-Index Notation
Section 2.3.7.6.4.3 - Einstein Notation
Section 2.3.7.6.4.4 - Ricci Calculus
Section 2.3.7.6.4.5 - Penrose Graphical Notation
Section 2.3.7.6.4.6 - Voigt Notation
Section 2.3.7.6.4.7 - Abstract Index Notation
Section 2.3.7.6.4.8 - Tetrad(Index) Notation
Section 2.3.7.6.4.9 - Van der Waerden Notation
Section 2.3.7.6.5 - Tensor Definitions
Section 2.3.7.6.5.1 - Tensor (Intrinsic Definition)
Section 2.3.7.6.5.2 - Tensor Field
Section 2.3.7.6.5.3 - Tensor Density
Section 2.3.7.6.5.4 - Tensors In Curvilinear Coordinates
Section 2.3.7.6.5.5 - Tensor Operator
Section 2.3.7.6.5.6 - Tensor Bundle
Section 2.3.7.6.5.7 - Two-Point Tensor
Section 2.3.7.6.6 - Some Noteable Tensors
Section 2.3.7.6.6.1 - Metric Tensor
Section 2.3.7.6.6.2 - Mixed Tensor
Section 2.3.7.6.6.3 - Symmetric Tensor
Section 2.3.7.6.6.4 - Antisymmetric Tensor
Section 2.3.7.6.6.5 - Dyadic Tensor
Section 2.3.7.6.6.6 - Kronecker Delta
Section 2.3.7.6.6.7 - Levi-Civita Symbol
Section 2.3.7.6.6.8 - Nonmetricity Tensor
Section 2.3.7.6.6.9 - Christoffel Symbols
Section 2.3.7.6.6.10 - Ricci Curvature
Section 2.3.7.6.6.11 - Riemann Curvature Tensor
Section 2.3.7.6.6.12 - Weyl Tensor
Section 2.3.7.6.6.13 - Torsion Tensor
Section 2.3.7.6.7 - Tensor Operations
Section 2.3.7.6.7.1 - Tensor Product
Section 2.3.7.6.7.2 - Tensor Contraction
Section 2.3.7.6.7.3 - Tensor Algebra
Section 2.3.7.6.7.3.0 - Basic Writeup - Wikipedia - Tensor Algebra
Section 2.3.7.6.7.3.1 - Exterior (Grassmann) Algebra
Section 2.3.7.6.7.3.1.0 - Basic Writeup - Exterior (Grassmann) Algebra
Section 2.3.7.6.7.3.1.1 - Exterior Product
Section 2.3.7.6.7.3.1.2 - Exterior Power
Section 2.3.7.6.7.3.2 - Symmetric Algebra
Section 2.3.7.6.7.3.3 - Clifford Algebra
Section 2.3.7.6.7.3.4 - Geometric Algebra
Section 2.3.7.6.7.4 - Transpose (2nd Order Tensors)
Section 2.3.7.6.7.5 - Raising and Lowering Indices
Section 2.3.7.6.7.6 - Hodge Star Operator
Section 2.3.7.6.7.7 - Covariant Derivative
Section 2.3.7.6.7.8 - Exterior Derivative
Section 2.3.7.6.7.9 - Exterior Covariant Derivative
Section 2.3.7.6.7.10 - Lie Derivative
Section 2.3.8 - Affine Space
Section 2.3.8.0 - Basic Writeup - Wikipedia - Affine Space
Section 2.3.8.1 - Affine transformation
Section 2.3.8.2 - Affine group
Section 2.3.8.3 - Affine geometry
Section 2.3.8.4 - Affine coordinate system
Section 2.3.8.5 - Flat (geometry)
Section 2.3.8.6 - Cartesian coordinate system
Section 2.3.8.7 - Euclidean group
Section 2.3.8.8 - Poincaré group
Section 2.3.8.9 - Galilean group
Section 2.3.9 - Projective Space
Section 2.3.9.0 - Basic Writeup - Wikipedia - Projective Space
Section 2.3.9.1 - Projective transformation
Section 2.3.9.2 - Projective geometry
Section 2.3.9.3 - Projective linear group
Section 2.3.9.4 - Quadric Section
Section 2.3.9.5 - Conic Section
Section 2.3.10 - Numerical Linear Algebra
Section 2.3.10.0 - Basic Writeup - Wikipedia - Numerical Linear Algebra
Section 2.3.10.1 - Basic Concepts in Numerical Linear Algebra
Section 2.3.10.1.1 - Types of matrices appearing in numerical analysis
Section 2.3.10.1.1.1 - Sparse matrix
Section 2.3.10.1.1.1.0 - Basic Writeup - Wikipedia - Sparse matrix
Section 2.3.10.1.1.1.1 - Band matrix
Section 2.3.10.1.1.1.2 - Bidiagonal matrix
Section 2.3.10.1.1.1.3 - Tridiagonal matrix
Section 2.3.10.1.1.1.4 - Pentadiagonal matrix
Section 2.3.10.1.1.1.5 - Skyline matrix
Section 2.3.10.1.1.2 - Circulant matrix
Section 2.3.10.1.1.3 - Triangular matrix
Section 2.3.10.1.1.4 - Diagonally dominant matrix
Section 2.3.10.1.1.5 - Block matrix
Section 2.3.10.1.1.6 - Stieltjes matrix
Section 2.3.10.1.1.7 - Hilbert matrix
Section 2.3.10.1.1.8 - Wilkinson matrix
Section 2.3.10.1.1.9 - Convergent matrix
Section 2.3.10.1.2 - Algorithms for matrix multiplication
Section 2.3.10.1.2.1 - Strassen algorithm
Section 2.3.10.1.2.2 - Coppersmith–Winograd algorithm
Section 2.3.10.1.2.3 - Cannon's algorithm
Section 2.3.10.1.2.4 - Freivalds' algorithm
Section 2.3.10.1.3 - Matrix decompositions (See Chapter 4.5.7.1 for Matrix Decomposition Details)
Section 2.3.10.2 - Solving Linear Systems of Equations
Section 2.3.10.2.0 - Basic Writeup - Wikibooks - Solving Linear Systems
Section 2.3.10.2.1 - Gauss' Method
Section 2.3.10.2.2 - Describing the Solution Set
Section 2.3.10.2.3 - General = Particular + Homogeneous
Section 2.3.10.2.4 - Comparing Set Descriptions
Section 2.3.10.2.5 - Automation
Section 2.3.10.2.6 - Gaussian elimination
Section 2.3.10.2.6.0 - Basic Writeup - Wikipedia - Gaussian elimination
Section 2.3.10.2.6.1 - Row echelon form
Section 2.3.10.2.6.2 - Bareiss algorithm
Section 2.3.10.2.6.3 - Tridiagonal matrix algorithm
Section 2.3.10.2.7 - Solving Linear Equations through Factorization(Decomposition - See Section 2.3.5.7)
Section 2.3.10.2.7.1 - LU decomposition
Section 2.3.10.2.7.1.0 - Basic Writeup - Wikipedia - LU decomposition
Section 2.3.10.2.7.1.1 - Crout matrix decomposition
Section 2.3.10.2.7.1.2 - LU reduction
Section 2.3.10.2.7.1.3 - Block LU decomposition
Section 2.3.10.2.7.2 - Rank Factorization
Section 2.3.10.2.7.3 - QR Decomp
Section 2.3.10.2.7.4 - RRQR Decomp
Section 2.3.10.2.7.5 - Interpolative Decomp
Section 2.3.10.2.7.6 - Cholesky decomposition
Section 2.3.10.2.7.6.0 - Basic Writeup - Wikipedia - Cholesky decomposition
Section 2.3.10.2.7.6.1 - Minimum degree algorithm
Section 2.3.10.2.7.6.2 - Symbolic Cholesky decomposition
Section 2.3.10.2.8 - Iterative refinement
Section 2.3.10.2.9 - Direct methods for sparse matrices
Section 2.3.10.2.9.1 - Frontal Solver
Section 2.3.10.2.9.2 - Nested dissection
Section 2.3.10.2.10 - Levinson recursion for Toeplitz matrices
Section 2.3.10.2.11 - SPIKE algorithm
Section 2.3.10.2.12 - Cyclic reduction
Section 2.3.10.2.13 - Iterative methods
Section 2.3.10.2.13.1 - Jacobi method
Section 2.3.10.2.13.2 - Gauss–Seidel method
Section 2.3.10.2.13.2.0 - Basic Writeup - Wikipedia - Gauss–Seidel method
Section 2.3.10.2.13.2.1 - Successive over-relaxation (SOR)
Section 2.3.10.2.13.2.1.0 - Basic Writeup - Wikipedia - Successive over-relaxation (SOR)
Section 2.3.10.2.13.2.1.1 - Symmetric successive overrelaxation (SSOR)
Section 2.3.10.2.13.2.2 - Backfitting algorithm
Section 2.3.10.2.13.3 - Modified Richardson iteration
Section 2.3.10.2.13.4 - Conjugate gradient method (CG)
Section 2.3.10.2.13.4.0 - Basic Writeup - Wikipedia - Conjugate gradient method (CG)
Section 2.3.10.2.13.4.1 - Derivation of the conjugate gradient method
Section 2.3.10.2.13.4.2 - Nonlinear conjugate gradient method
Section 2.3.10.2.13.5 - Biconjugate gradient method (BiCG)
Section 2.3.10.2.13.5.0 - Basic Writeup - Wikipedia - Biconjugate gradient method (BiCG)
Section 2.3.10.2.13.5.1 - Biconjugate Gradient Stabilized Method(BiCGSTAB)
Section 2.3.10.2.13.6 - Conjugate residual method
Section 2.3.10.2.13.7 - Generalized minimal residual method (GMRES)
Section 2.3.10.2.13.8 - Chebyshev iteration
Section 2.3.10.2.13.9 - Stone's method (SIP – Srongly Implicit Procedure)
Section 2.3.10.2.13.10 - Kaczmarz method
Section 2.3.10.2.13.11 - Preconditioner
Section 2.3.10.2.13.11.0 - Basic Writeup - Wikipedia - Preconditioner
Section 2.3.10.2.13.11.1 - Incomplete Cholesky factorization
Section 2.3.10.2.13.11.2 - Incomplete LU factorization
Section 2.3.10.2.13.12 - Uzawa iteration
Section 2.3.10.2.14 - Underdetermined and overdetermined systems
Section 2.3.10.2.14.1 - Numerical computation of null space
Section 2.3.10.2.14.2 - Moore–Penrose pseudoinverse
Section 2.3.10.2.14.3 - Sparse approximation
Section 2.3.10.3 - Eigenvalue Algorithms
Section 2.3.10.3.0 - Basic Writeup - Wikipedia - Eigenvalue Algorithms
Section 2.3.10.3.1 - Power iteration
Section 2.3.10.3.2 - Inverse iteration
Section 2.3.10.3.3 - Rayleigh quotient iteration
Section 2.3.10.3.4 - Arnoldi iteration
Section 2.3.10.3.5 - Lanczos algorithm
Section 2.3.10.3.5.0 - Basic Writeup - Wikipedia - Lanczos algorithm
Section 2.3.10.3.5.1 - Block Lanczos algorithm
Section 2.3.10.3.6 - QR algorithm
Section 2.3.10.3.7 - Jacobi eigenvalue algorithm
Section 2.3.10.3.7.0 - Basic Writeup - Wikipedia - Jacobi eigenvalue algorithm
Section 2.3.10.3.7.1 - Jacobi rotation
Section 2.3.10.3.7.2 - Jacobi method for complex Hermitian matrices
Section 2.3.10.3.8 - Divide-and-conquer eigenvalue algorithm
Section 2.3.10.3.9 - Folded spectrum method
Section 2.3.10.3.10 - Locally Optimal Block Preconditioned Conjugate Gradient Method(LOBPCG)
Section 2.3.10.3.11 - Eigenvalue perturbation
Section 2.3.10.4 - Other Concepts and Algorithms
Section 2.3.10.4.1 - Orthogonalization algorithms
Section 2.3.10.4.1.0 - Basic Writeup - Wikipedia - Orthogonalization algorithms
Section 2.3.10.4.1.1 - Gram–Schmidt process
Section 2.3.10.4.1.2 - Householder transformation
Section 2.3.10.4.1.2.0 - Basic Writeup - Wikipedia - Householder transformation
Section 2.3.10.4.1.2.1 - Householder operator
Section 2.3.10.4.1.3 - Givens rotation
Section 2.3.10.4.2 - Krylov subspace
Section 2.3.10.4.3 - Block matrix pseudoinverse
Section 2.3.10.4.4 - Bidiagonalization
Section 2.3.10.4.5 - Cuthill–McKee algorithm
Section 2.3.10.4.6 - In-place matrix transposition
Section 2.3.10.4.7 - Pivot element
Section 2.3.10.4.8 - Matrix-free methods
