Outline of linear algebra: Difference between revisions
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<noinclude>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. |
<noinclude>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. |
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==Linear equations== |
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[[Linear equation]] |
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*[[System of linear equations]] |
*[[System of linear equations]] |
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*[[Determinant]] |
*[[Determinant]] |
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==Matrices== |
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[[Matrix (mathematics)|Matrix]] |
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*[[Matrix addition]] |
*[[Matrix addition]] |
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*[[Matrix multiplication]] |
*[[Matrix multiplication]] |
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==Matrix decompositions== |
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[[Matrix decomposition]] |
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*[[Cholesky decomposition]] |
*[[Cholesky decomposition]] |
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*[[LU decomposition]] |
*[[LU decomposition]] |
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*[[Woodbury matrix identity]] |
*[[Woodbury matrix identity]] |
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==Vector spaces== |
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[[Vector space]] |
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*[[Linear combination]] |
*[[Linear combination]] |
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*[[Linear span]] |
*[[Linear span]] |
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* [[Symplectic structure]] |
* [[Symplectic structure]] |
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==Multilinear algebra== |
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[[Multilinear algebra]] |
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*[[Tensor]] |
*[[Tensor]] |
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**[[Classical treatment of tensors]] |
**[[Classical treatment of tensors]] |
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**[[Geometric algebra]] |
**[[Geometric algebra]] |
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==Topics related to affine spaces== |
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[[Affine space]] |
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*[[Affine transformation]] |
*[[Affine transformation]] |
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*[[Affine group]] |
*[[Affine group]] |
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*[[Galilean group]] |
*[[Galilean group]] |
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==Projective space== |
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[[Projective space]] |
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*[[Projective transformation]] |
*[[Projective transformation]] |
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*[[Projective geometry]] |
*[[Projective geometry]] |
Revision as of 13:53, 5 April 2022
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
Matrices
Matrix
- 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
Relations
Computations
- Elementary row operations
- Householder transformation
- Least squares, linear least squares
- Gram–Schmidt process
- Woodbury matrix identity
Vector spaces
Vector space