Outline of linear algebra: Difference between revisions
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{{short description|Wikipedia list article}} |
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This is a list of '''[[linear algebra]] topics'''. See also: |
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part of the set of 830+ outlines listed at |
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*[[List of matrices]] |
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[[Wikipedia:Contents/Outlines]]. |
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a special type of list article. |
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They make up one of Wikipedia's |
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See [[Wikipedia: Outlines]] and |
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{{Short description|None}} |
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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. |
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==Linear equations== |
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*[[System of linear equations]] |
*[[System of linear equations]] |
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*[[Determinant]] |
*[[Determinant]] |
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*[[Gaussian elimination]] |
*[[Gaussian elimination]] |
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*[[Gauss–Jordan elimination]] |
*[[Gauss–Jordan elimination]] |
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*[[Overcompleteness]] |
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*[[Strassen algorithm]] |
*[[Strassen algorithm]] |
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}} |
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==Matrices== |
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*[[Matrix addition]] |
*[[Matrix addition]] |
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*[[Matrix multiplication]] |
*[[Matrix multiplication]] |
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**[[Hankel matrix]] |
**[[Hankel matrix]] |
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**[[(0,1)-matrix]] |
**[[(0,1)-matrix]] |
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}} |
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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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*[[QR decomposition]] |
*[[QR decomposition]] |
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*[[Polar decomposition]] |
*[[Polar decomposition]] |
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*[[Reducing subspace]] |
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*[[Spectral theorem]] |
*[[Spectral theorem]] |
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*[[Singular value decomposition]] |
*[[Singular value decomposition]] |
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**[[Schur complement]] |
**[[Schur complement]] |
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**[[Haynsworth inertia additivity formula]] |
**[[Haynsworth inertia additivity formula]] |
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}} |
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==Relations== |
==Relations== |
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*[[Matrix equivalence]] |
*[[Matrix equivalence]] |
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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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**[[Linear functional]] |
**[[Linear functional]] |
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*[[Category of vector spaces]] |
*[[Category of vector spaces]] |
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}} |
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==Structures== |
==Structures== |
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*[[Topological vector space]] |
*[[Topological vector space]] |
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*[[Normed vector space]] |
*[[Normed vector space]] |
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**[[Improper rotation]] |
**[[Improper rotation]] |
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* [[Symplectic structure]] |
* [[Symplectic structure]] |
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}} |
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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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**[[Component-free treatment of tensors]] |
**[[Component-free treatment of tensors]] |
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**[[Gamas's Theorem]] |
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*[[Outer product]] |
*[[Outer product]] |
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*[[Tensor algebra]] |
*[[Tensor algebra]] |
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**[[Clifford algebra]] |
**[[Clifford algebra]] |
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**[[Geometric algebra]] |
**[[Geometric algebra]] |
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}} |
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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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*[[Poincaré group]] |
*[[Poincaré group]] |
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*[[Galilean group]] |
*[[Galilean group]] |
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}} |
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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]] |
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*[[Projective linear group]] |
*[[Projective linear group]] |
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*[[Quadric]] and [[conic section]] |
*[[Quadric]] and [[conic section]] |
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==See also== |
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{{Linear algebra}} |
{{Linear algebra}} |
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[[Category:Mathematics-related lists|Linear algebra]] |
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[[Category:Linear algebra|*]] |
[[Category:Linear algebra|*]] |
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[[Category:Outlines of mathematics and logic|Linear algebra]] |
[[Category:Outlines of mathematics and logic|Linear algebra]] |
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[[Category: |
[[Category:Outlines|Linear algebra]] |
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[[Category:Lists of topics|Linear algebra]] |
Latest revision as of 12:12, 30 October 2023
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
[edit]- System of linear equations
- Determinant
- Cramer's rule
- Gaussian elimination
- Gauss–Jordan elimination
- Overcompleteness
- Strassen algorithm
Matrices
[edit]- 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
[edit]- Cholesky decomposition
- LU decomposition
- QR decomposition
- Polar decomposition
- Reducing subspace
- Spectral theorem
- Singular value decomposition
- Schur decomposition
Relations
[edit]Computations
[edit]- Elementary row operations
- Householder transformation
- Least squares, linear least squares
- Gram–Schmidt process
- Woodbury matrix identity
Vector spaces
[edit]- 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
[edit]- Topological vector space
- Normed vector space
- Inner product space
- Pseudo-Euclidean space
- Orientation (geometry)
- Symplectic structure
Multilinear algebra
[edit]Topics related to affine spaces
[edit]- Affine transformation
- Affine group
- Affine geometry
- Affine coordinate system
- Flat (geometry)
- Cartesian coordinate system
- Euclidean group
- Poincaré group
- Galilean group