ⓘ List of linear algebra topics

                                     

ⓘ List of linear algebra topics

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

1. Matrix decompositions

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

2. Vector spaces

  • Linear span
  • Linear independence
  • Linear combination
  • Change of basis
  • Scalar multiplication
  • Basis
  • Hamel basis
  • Hamel dimension
  • Dimension theorem for vector spaces
  • Cyclic decomposition theorem
  • Examples of vector spaces
  • Linear map
  • Squeeze mapping or Lorentz transformation
  • Shear mapping or Galilean transformation
  • Linear subspace
  • Nullity theorem
  • Rank–nullity theorem
  • Row space
  • Cyclic subspace
  • Row and column spaces
  • Null space, nullity
  • Column space
  • Linear functional
  • Dual space
  • Linear function
  • Category of vector spaces
                                     

3. Structures

  • Orthogonal group
  • Inner product space
  • Orthogonal complement
  • Orthogonal projection
  • Orthogonality
  • Euclidean space
  • Topological vector space
  • Normed vector space
  • Pseudo-Euclidean space
  • Indefinite orthogonal group
  • Null vector
  • Improper rotation
  • Orientation geometry
  • Symplectic structure
                                     

4. Multilinear algebra

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

5. Affine space and related topics

  • Poincare group
  • Affine group
  • Flat geometry
  • Affine transformation
  • Affine coordinate system
  • Cartesian coordinate system
  • Affine geometry
  • Galilean group
  • Euclidean group
                                     
  • algebra topics List of homological algebra topics List of linear algebra topics List of algebraic structures Glossary of field theory Glossary of group
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