List of linear algebra topics
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This is a list of linear algebra topics.
Linear equations[]
Matrices[]
- Matrix theory
- Matrix addition
- Matrix multiplication
- Basis transformation matrix
- Characteristic polynomial
- Trace
- Eigenvalue, eigenvector and eigenspace
- Rank
- Matrix inversion, invertible matrix
- Pseudoinverse
- Adjugate
- Transpose
- Positive-definite, positive-semidefinite matrix
- Pfaffian
- Projection
- Spectral theorem
- Perron–Frobenius theorem
- List of matrices
Matrix decompositions[]
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
- 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[]
- Topological vector space
- Normed vector space
- Inner product space
- Euclidean space
- Orthogonality
- Orthogonal complement
- Orthogonal projection
- Orthogonal group
- Pseudo-Euclidean space
- Orientation (geometry)
- Symplectic structure
Multilinear algebra[]
- Tensor
- Classical treatment of tensors
- Component-free treatment of tensors
- Outer product
- Tensor algebra
[]
Projective space[]
- Projective transformation
- Projective geometry
- Projective linear group
- Quadric and conic section
See also[]
- Glossary of linear algebra
- Glossary of tensor theory
| Basic concepts |  | |
|---|---|---|
| Matrices | ||
| Bilinear | ||
| Multilinear algebra | ||
| Vector space constructions |
| |
| Numerical | ||
| ||
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