List of linear algebra topics
This is a list of linear algebra topics. See also:
Linear equations
- System of linear equations
- Determinant
- Cramer's rule
- Gaussian elimination
- Gauss–Jordan elimination
- Strassen algorithm
Matrices
- 2 × 2 real matrices
- Matrix theory
- 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
- 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 space and related topics
- Affine transformation
- Affine group
- Affine geometry
- Affine coordinate system
- Flat (geometry)
- Cartesian coordinate system
- Euclidean group
- Poincaré group
- Galilean group
Projective space
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