Outline of linear algebra
Template:Short description This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices.
Linear equations
- System of linear equations
- Determinant
- Cramer's rule
- Gaussian elimination
- Gauss–Jordan elimination
- Overcompleteness
- Strassen algorithm
Matrices
- Matrix addition
- Matrix multiplication
- Basis transformation matrix
- Characteristic polynomial
- Trace
- Eigenvalue, eigenvector and eigenspace
- Rank
- Matrix inversion, invertible matrix
- Adjugate
- Transpose
- Positive-definite, positive-semidefinite matrix
- Pfaffian
- Projection
- Spectral theorem
- Perron–Frobenius theorem
- List of matrices
Matrix decompositions
- Cholesky decomposition
- LU decomposition
- QR decomposition
- Polar decomposition
- Reducing subspace
- Spectral theorem
- Singular value decomposition
- Schur decomposition
Relations
Computations
- Elementary row operations
- Householder transformation
- Least squares, linear least squares
- Gram–Schmidt process
- Woodbury matrix identity
Vector spaces
- Linear combination
- Linear span
- Linear independence
- Scalar multiplication
- Basis
- Cyclic decomposition theorem
- Dimension theorem for vector spaces
- Examples of vector spaces
- Linear map
- Linear subspace
- Dual space
- Category of vector spaces
Structures
- Topological vector space
- Normed vector space
- Inner product space
- Pseudo-Euclidean space
- Orientation (geometry)
- Symplectic structure
Multilinear algebra
- Affine transformation
- Affine group
- Affine geometry
- Affine coordinate system
- Flat (geometry)
- Cartesian coordinate system
- Euclidean group
- Poincaré group
- Galilean group
Projective space
See also
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