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Linear algebra

| nosplit | ↑ parent "Algebra" | words: 0 | descendant words: 6k | descendants: 114

nosplit | ⇓ toc | ↑ parent "Algebra" | Wikipedia | words: 0 | descendant words: 6k | descendants: 114

Table of contents | 0, 6k, 114
- Linear function | 131 | 🔗 link | nosplit | ↑ parent "Linear algebra"
- Linear map (linear operator) | 313, 2k, 27 | 🔗 link | nosplit | ↑ parent "Linear algebra"
  - Form (mathematics) | 54 | 🔗 link | nosplit | ↑ parent "Linear map"
  - Linear form | 64, 497, 3 | 🔗 link | nosplit | ↑ parent "Linear map"
    - Matrix representation of a linear form | 49 | 🔗 link | nosplit | ↑ parent "Linear form"
    - Dual space ( $V^{*}$ ) | 165, 384, 1 | 🔗 link | nosplit | ↑ parent "Linear form"
      - Dual vector ( $e^{i}$ ) | 219 | 🔗 link | nosplit | ↑ parent "Dual space"
  - Linear operator | 122, 177, 1 | 🔗 link | nosplit | ↑ parent "Linear map"
    - Adjoint operator ( $A^{†}$ ) | 55 | 🔗 link | nosplit | ↑ parent "Linear operator"
  - Self-adjoint operator | 🔗 link | nosplit | ↑ parent "Linear map"
  - Multilinear map | 0, 1k, 18 | 🔗 link | nosplit | ↑ parent "Linear map"
    - Bilinear map | 133 | 🔗 link | nosplit | ↑ parent "Multilinear map"
    - Bilinear form ( $B (x, y)$ ) | 105, 419, 2 | 🔗 link | nosplit | ↑ parent "Multilinear map"
      - Matrix representation of a bilinear form | 113, 314, 1 | 🔗 link | nosplit | ↑ parent "Bilinear form"
        
        Effect of a change of basis on the matrix of a bilinear form ( $B_{2} = C^{T} B C$ ) | 201 | 🔗 link | nosplit | ↑ parent "Matrix representation of a bilinear form"
    - Multilinear form | 59 | 🔗 link | nosplit | ↑ parent "Multilinear map"
    - Symmetric bilinear map | 63, 578, 9 | 🔗 link | nosplit | ↑ parent "Multilinear map"
      - Symmetric bilinear form | 18, 120, 1 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
        
        Matrix representation of a symmetric bilinear form | 102 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear form"
      - Hermitian form | 89, 99, 1 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
        
        Matrix representation of a Hermitian form | 10 | 🔗 link | nosplit | ↑ parent "Hermitian form"
      - Quadratic form | 223 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
      - Positive definite symmetric bilinear form | 19, 39, 1 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
        
        Matrix representation of a positive definite symmetric bilinear form | 20 | 🔗 link | nosplit | ↑ parent "Positive definite symmetric bilinear form"
      - Skew-symmetric bilinear map | 16 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
      - Skew-symmetric bilinear form | 18 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
    - Symmetric multilinear map | 8, 16, 1 | 🔗 link | nosplit | ↑ parent "Multilinear map"
      - Antisymmetric multilinear map | 8 | 🔗 link | nosplit | ↑ parent "Symmetric multilinear map"
    - Alternating multilinear map | 9 | 🔗 link | nosplit | ↑ parent "Multilinear map"
- Dot product | 295, 295, 3 | 🔗 link | nosplit | ↑ parent "Linear algebra"
  - Orthogonality | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Dot product"
    - Orthonormality | 🔗 link | nosplit | ↑ parent "Orthogonality"
  - Angle | 🔗 link | nosplit | ↑ parent "Dot product"
- Cross product ( $x \times y$ ) | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Linear algebra"
  - Jacobi identity | 🔗 link | nosplit | ↑ parent "Cross product"
- Index picking function | 0, 158, 3 | 🔗 link | nosplit | ↑ parent "Linear algebra"
  - Kronecker delta ( $δ_{i j}$ ) | 🔗 link | nosplit | ↑ parent "Index picking function"
  - Levi-Civita symbol ( $ε$ ) | 61, 158, 1 | 🔗 link | nosplit | ↑ parent "Index picking function"
    - Levi-Civita symbol as a tensor | 97 | 🔗 link | nosplit | ↑ parent "Levi-Civita symbol"
- Projection (mathematics) | 🔗 link | nosplit | ↑ parent "Linear algebra"
- Matrix | 0, 2k, 44 | 🔗 link | nosplit | ↑ parent "Linear algebra"
  - Matrix operation | 0, 146, 6 | 🔗 link | nosplit | ↑ parent "Matrix"
    - Determinant ( $d e t$ ) | 30 | 🔗 link | nosplit | ↑ parent "Matrix operation"
    - Matrix inverse ( $M^{- 1}$ ) | 24, 73, 1 | 🔗 link | nosplit | ↑ parent "Matrix operation"
      - Invertible matrix | 49 | 🔗 link | nosplit | ↑ parent "Matrix inverse"
    - Transpose ( $M^{T}$ ) | 0, 43, 2 | 🔗 link | nosplit | ↑ parent "Matrix operation"
      - Transpose of a matrix multiplication | 22 | 🔗 link | nosplit | ↑ parent "Transpose"
      - Inverse of the transpose | 21 | 🔗 link | nosplit | ↑ parent "Transpose"
  - Matrix multiplication | 80, 84, 2 | 🔗 link | nosplit | ↑ parent "Matrix"
    - Matrix multiplication algorithm | 4 | 🔗 link | nosplit | ↑ parent "Matrix multiplication"
    - Matrix decomposition | 🔗 link | nosplit | ↑ parent "Matrix multiplication"
  - Eigenvalues and eigenvectors | 0, 1k, 18 | 🔗 link | nosplit | ↑ parent "Matrix"
    - Applications of eigenvalues and eigenvectors | 12 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
    - Eigenvalue | 9, 130, 2 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
      - Spectrum (functional analysis) | 18, 121, 1 | 🔗 link | nosplit | ↑ parent "Eigenvalue"
        
        Continuous spectrum (functional analysis) | 103 | 🔗 link | nosplit | ↑ parent "Spectrum"
    - Eigendecomposition of a matrix | 128, 794, 7 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
      - Eigendecomposition of a real symmetric matrix | 40 | 🔗 link | nosplit | ↑ parent "Eigendecomposition of a matrix"
      - Sylvester's law of inertia | 527, 626, 5 | 🔗 link | nosplit | ↑ parent "Eigendecomposition of a matrix"
        
        Congruent matrix | 36, 99, 1 | 🔗 link | nosplit | ↑ parent "Sylvester's law of inertia"
        
        Matrix congruence can be seen as the change of basis of a bilinear form | 63 | 🔗 link | nosplit | ↑ parent "Congruent matrix"
        
        Matrix similarity | 🔗 link | nosplit | ↑ parent "Sylvester's law of inertia"
        
        Metric signature | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Sylvester's law of inertia"
        
        Metric signature matrix | 🔗 link | nosplit | ↑ parent "Metric signature"
    - Eigenvector | 9 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
    - Eigenvectors and eigenvalues of the identity matrix | 4 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
    - Spectral theorem | 0, 63, 3 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
      - Hermitian matrix | 0, 63, 2 | 🔗 link | nosplit | ↑ parent "Spectral theorem"
        
        Hermitian operator | 63, 63, 1 | 🔗 link | nosplit | ↑ parent "Hermitian matrix"
        
        Riesz representation theorem | 🔗 link | nosplit | ↑ parent "Hermitian operator"
  - Kronecker product | 🔗 link | nosplit | ↑ parent "Matrix"
  - Named matrix | 0, 284, 13 | 🔗 link | nosplit | ↑ parent "Matrix"
    - Diagonal matrix | 19, 38, 2 | 🔗 link | nosplit | ↑ parent "Named matrix"
      - Scalar matrix ( $Z (V)$ ) | 19, 19, 1 | 🔗 link | nosplit | ↑ parent "Diagonal matrix"
        
        Identity matrix ( $I_{n}$ ) | 🔗 link | nosplit | ↑ parent "Scalar matrix"
    - Square matrix | 0, 53, 1 | 🔗 link | nosplit | ↑ parent "Named matrix"
      - Matrix ring (Matrix ring of degree n, $M_{n}$ , Set of all n-by-y square matrices) | 53 | 🔗 link | nosplit | ↑ parent "Square matrix"
    - Orthogonal matrix | 11, 56, 1 | 🔗 link | nosplit | ↑ parent "Named matrix"
      - Unitary matrix | 45 | 🔗 link | nosplit | ↑ parent "Orthogonal matrix"
    - Triangular matrix | 🔗 link | nosplit | ↑ parent "Named matrix"
    - Symmetric matrix | 54, 137, 4 | 🔗 link | nosplit | ↑ parent "Named matrix"
      - Definite matrix | 16, 55, 1 | 🔗 link | nosplit | ↑ parent "Symmetric matrix"
        
        Positive definite matrix | 39 | 🔗 link | nosplit | ↑ parent "Definite matrix"
      - Skew-symmetric matrix (Antisymmetric matrix) | 28, 28, 1 | 🔗 link | nosplit | ↑ parent "Symmetric matrix"
        
        Skew-symmetric form | 🔗 link | nosplit | ↑ parent "Skew-symmetric matrix"
- Vector space | 0, 394, 9 | 🔗 link | nosplit | ↑ parent "Linear algebra"
  - Basis (linear algebra) | 0, 235, 4 | 🔗 link | nosplit | ↑ parent "Vector space"
    - Change of basis | 25, 235, 2 | 🔗 link | nosplit | ↑ parent "Basis"
      - Change of basis matrix | 165 | 🔗 link | nosplit | ↑ parent "Change of basis"
      - Change of basis between symmetric matrices | 45 | 🔗 link | nosplit | ↑ parent "Change of basis"
    - Linear independence | 🔗 link | nosplit | ↑ parent "Basis"
  - Classification of vector spaces | 4 | 🔗 link | nosplit | ↑ parent "Vector space"
  - Underlying field of a vector space | 114 | 🔗 link | nosplit | ↑ parent "Vector space"
  - Vector (mathematics) | 0, 41, 1 | 🔗 link | nosplit | ↑ parent "Vector space"
    - Scalar (mathematics) | 41 | 🔗 link | nosplit | ↑ parent "Vector"
- Tensor | 124, 990, 17 | 🔗 link | nosplit | ↑ parent "Linear algebra"
  - A linear map is a (1,1) tensor | 80 | 🔗 link | nosplit | ↑ parent "Tensor"
  - Tensor space ( $T^{(m, n)}$ ) | 5, 11, 1 | 🔗 link | nosplit | ↑ parent "Tensor"
    - Order of a tensor | 6 | 🔗 link | nosplit | ↑ parent "Tensor space"
  - Einstein notation (Einstein summation convention) | 103, 775, 13 | 🔗 link | nosplit | ↑ parent "Tensor"
    - Raised and lowered indices | 109, 109, 3 | 🔗 link | nosplit | ↑ parent "Einstein notation"
    - Implicit metric signature in Einstein notation | 79 | 🔗 link | nosplit | ↑ parent "Einstein notation"
    - Einstein notation for partial derivatives | 102, 484, 4 | 🔗 link | nosplit | ↑ parent "Einstein notation"
      - Divergence in Einstein notation | 125 | 🔗 link | nosplit | ↑ parent "Einstein notation for partial derivatives"
      - Laplacian in Einstein notation ( $\partial_{i} \partial^{i}$ ) | 108, 257, 2 | 🔗 link | nosplit | ↑ parent "Einstein notation for partial derivatives"
        
        D'alembert operator in Einstein notation ( $\partial_{i} \partial^{i}$ ) | 96, 149, 1 | 🔗 link | nosplit | ↑ parent "Laplacian in Einstein notation"
        
        Klein-Gordon equation in Einstein notation | 53 | 🔗 link | nosplit | ↑ parent "D'alembert operator in Einstein notation"
    - Covariance and contravariance of vectors | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Einstein notation"
      - Covariant vector | 🔗 link | nosplit | ↑ parent "Covariance and contravariance of vectors"
      - Contravariant vector | 🔗 link | nosplit | ↑ parent "Covariance and contravariance of vectors"
- Linear algebra bibliography | 23 | 🔗 link | nosplit | ↑ parent "Linear algebra"

Ancestors

Algebra | 27, 11k, 216
Mathematics | 17, 34k, 763
Ciro Santilli's Homepage | 262, 238k, 4k

Incoming links

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