List of linear algebra topics

This is a list of linear algebra topics. See also

• list of matrices
• glossary of tensor theory.

Linear equations

• System of linear equations
• Determinant
  • Minor
  • Cauchy–Binet formula
• Cramer's rule
• Gaussian elimination
• Gauss–Jordan elimination
• Strassen algorithm

Matrices

• Matrix theory
• Matrix addition
• Matrix multiplication
• Basis transformation matrix
• Characteristic polynomial
• Trace
• Eigenvalue, eigenvector and eigenspace
  • Cayley–Hamilton theorem
  • Spread of a matrix
• Jordan normal form
• Rank
• Matrix inversion, invertible matrix
  • Pseudoinverse
• Adjugate
• Transpose
  • Dot product
  • Symmetric matrix
  • Matrix congruence
    • Congruence relation
  • Orthogonal matrix
  • Skew-symmetric matrix
  • Conjugate transpose
    • Unitary matrix
    • Hermitian matrix, Antihermitian
• Positive definite, positive semidefinite, positive-definite matrix
• Pfaffian
• Projection
• 2 × 2 real matrices
• Similar matrix
• Spectral theorem
• Woodbury matrix identity
• Perron–Frobenius theorem
• List of matrices
  • Diagonal matrix, main diagonal
    • Diagonalizable matrix
  • Triangular matrix
  • Tridiagonal matrix
  • Block matrix
  • Sparse matrix
  • Hessenberg matrix
  • Hessian matrix
  • Vandermonde matrix
  • Stochastic matrix
  • Toeplitz matrix
    • Circulant matrix
  • Hankel matrix
  • (0,1)-matrix

Matrix decompositions

• Cholesky decomposition
• LU decomposition
• QR decomposition
• Spectral theorem
• Singular value decomposition
  • Higher-order singular value decomposition
• Schur decomposition
  • Schur complement
  • Haynsworth inertia additivity formula

Computations

• Householder transformation
• Least squares, linear least squares
• Gram–Schmidt process

Vectors

• Scalar multiplication
• Linear combination
• Linear span
• Linear independence
• Basis
• Coordinates vector

Vector spaces

• Basis
  • Change of basis
  • Hamel basis
• Dimension theorem for vector spaces
  • Hamel dimension
• Examples of vector spaces
• Linear map
  • Shear mapping or Galilean transformation
  • Squeeze mapping or Lorentz transformation
• Column space
• Row space
• Null space, nullity
• Rank-nullity theorem
• Nullity theorem
• Dual space
  • Linear function
  • Linear functional
• Orthogonality
• Orthogonal complement
• Orthogonal projection
• Outer product
• Improper rotation
• Category of vector spaces
• Linear subspace
  • Euclidean subspace
• Normed vector space
• Inner product space

Multilinear algebra

• Tensor
  • Classical treatment of tensors
  • Intermediate treatment of tensors
  • Component-free treatment of tensors
• Tensor algebra
  • Exterior algebra
  • Symmetric algebra
  • Clifford algebra
  • Geometric algebra

Affine space

• Affine transformation
• Affine group
• Affine geometry

Projective space

• Projective transformation
• Projective geometry
• Quadric