List of linear algebra topics - Definition

This is a list of linear algebra topics, by Wikipedia page. See also

• list of matrices
• glossary of matrix theory
• glossary of tensor theory.

Linear equations

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

Matrices

• Matrix theory
• Matrix addition
• Matrix multiplication
• Basis transformation matrix
• Characteristic polynomial
• Trace (matrix), trace
• Cayley-Hamilton theorem
• Eigenvalue, eigenvector
• Jordan normal form
• Rank (matrix theory)
• Matrix inversion, invertible matrix
  • Pseudoinverse
• Adjugate
• Transpose
  • Dot product
  • Symmetric matrix
  • Orthogonal matrix
  • Skew-symmetric matrix
  • Conjugate transpose
    • Unitary matrix
    • Hermitian matrix, Antihermitian
• Positive definite, positive semidefinite, positive-definite matrix
• Pfaffian
• Projection (linear algebra)
• Diagonal matrix, main diagonal
  • Diagonalizable matrix
• Tridiagonal matrix
• Hessenberg matrix
• Triangular matrix
• Spectral theorem
• Stochastic matrix
• Toeplitz matrix
• Hankel matrix
• Vandermonde matrix
• Block matrix
• (0,1)-matrix
• Sparse matrix
• Payoff matrix
• Woodbury matrix identity
• Perron-Frobenius theorem

Matrix decompositions

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

Computations

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

Vectors

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

Vector spaces

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

Affine space

• Affine transformation
• Affine group
• Affine geometry

Projective space

• Projective transformation
• Projective geometry
• Quadric