• glossary of linear algebra,
• list of matrices
• glossary of matrix theory
• glossary of tensor theory.

Table of contents

1 Linear equations 2 Matrices 3 Matrix decompositions 4 Computations 5 Vectorss 6 Vector spaces 7 Multilinear algebra 8 Affine space

Linear equations

• System of linear equations
• Determinant
  • Minor (linear algebra)
  • Cauchy-Binet formula
• Cramer's rule
• Gauss-Jordan elimination

• Matrix theory
• Matrix addition
• Matrix multiplication
• Characteristic polynomial
• Trace (matrix), trace
• Cayley-Hamilton theorem
• Eigenvalue, eigenvector
• Jordan normal form
• Rank (matrix theory)
• Matrix inversion, invertible matrix
  • Pseudodinverse
• Adjugate
• Transpose
  • Dot product
  • Symmetric matrix
  • Orthogonal matrix
  • Skew-symmetric matrix
  • Conjugate transpose
    • Unitary matrix
    • Hermitian matrix
• Positive definite, positive semidefinite
• Diagonal matrix, main diagonal
  • Diagonalizable
• Triangular matrix
• Spectral theorem
• Stochastic matrix
• Toeplitz matrix
• Hankel matrix
• Vandermonde matrix
• Block matrix
• Sparse matrix
• Payoff matrix
• Woodbury matrix identity

• Cholesky decomposition
• LU decomposition
• QR decomposition
• Singular value decomposition
• Schur decomposition
  • Schur complement

• Householder transformation
• Least squares, linear least squares

• Scalar multiplication
• Linear combination
• Linear span
• Linear independence
• Basis (linear algebra)

• Basis (linear algebra)=Hamel basis
• Dimension theorem for vector spaces=Hamel dimension
• Examples
  • Vector space example 1
  • Vector space example 2
  • Vector space example 3
• Linear transformation
  • Galilean transformation, Lorentz transformation
• Column space
• Row space
• Null space, nullity
• Rank-nullity theorem
• Dual space
  • Linear function
  • Linear functional
• Orthogonality
• Orthogonal projection
• Improper rotation
• Category of vector spaces

• Tensor
  • Classical treatment of tensors
  • Intermediate treatment of tensors
  • Component-free treatment of tensors