Outline of linear algebra
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Linear equations
Matrices
- Matrix addition
- Matrix multiplication
- Basis transformation matrix
- Characteristic polynomial
- Trace
- Eigenvalue, eigenvector and eigenspace
- Cayley–Hamilton theorem
- Spread of a matrix
- Jordan normal form
- Weyr canonical form
- Rank
- Matrix inversion, invertible matrix
- Pseudoinverse
- Adjugate
- Transpose
- Dot product
- Symmetric matrix
- Orthogonal matrix
- Skew-symmetric matrix
- Conjugate transpose
- Unitary matrix
- Hermitian matrix, Antihermitian matrix
- Positive-definite, positive-semidefinite matrix
- Pfaffian
- Projection
- Spectral theorem
- 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
Relations
Computations
Vector spaces
- Linear combination
- Linear span
- Linear independence
- Scalar multiplication
- Basis
- Change of basis
- Hamel basis
- Cyclic decomposition theorem
- Dimension theorem for vector spaces
- Hamel dimension
- Examples of vector spaces
- Linear map
- Shear mapping or Galilean transformation
- Squeeze mapping or Lorentz transformation
- Linear subspace
- Row and column spaces
- Column space
- Row space
- Cyclic subspace
- Null space, nullity
- Rank–nullity theorem
- Nullity theorem
- Dual space
- Linear function
- Linear functional
- Category of vector spaces
Structures
Multilinear algebra
Projective space
See also
{{Linear algebra}}