Editing Outline of linear algebra

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{{Short description|None}}
<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.

==Linear equations==
[[Linear equation]]
*[[System of linear equations]]
*[[Determinant]]
**[[Minor (linear algebra)|Minor]]
**[[Cauchy–Binet formula]]
*[[Cramer's rule]]
*[[Gaussian elimination]]
*[[Gauss–Jordan elimination]]
*[[Overcompleteness]]
*[[Strassen algorithm]]

==Matrices==
[[Matrix (mathematics)|Matrix]]
*[[Matrix addition]]
*[[Matrix multiplication]]
*[[Basis transformation matrix]]
*[[Characteristic polynomial]]
*[[Trace (matrix)|Trace]]
*[[Eigenvalue, eigenvector and eigenspace]]
**[[Cayley–Hamilton theorem]]
**[[Spread of a matrix]]
**[[Jordan normal form]]
**[[Weyr canonical form]]
*[[Rank (matrix theory)|Rank]]
*[[Matrix inversion]], [[invertible matrix]]
**[[Pseudoinverse]]
*[[Adjugate]]
*[[Transpose]]
**[[Dot product]]
**[[Symmetric matrix]]
**[[Orthogonal matrix]]
**[[Skew-symmetric matrix]]
**[[Conjugate transpose]]
***[[Unitary matrix]]
***[[Hermitian matrix]], [[Antihermitian matrix]]
*[[Positive-definite matrix|Positive-definite]], [[positive-semidefinite matrix]]
*[[Pfaffian]]
*[[Projection (linear algebra)|Projection]]
*[[Spectral theorem]]
*[[Perron–Frobenius theorem]]
*[[List of matrices]]
**[[Diagonal matrix]], [[main diagonal]]
***[[Diagonalizable matrix]]
**[[Triangular matrix]]
**[[Tridiagonal matrix]]
**[[Block matrix]]
**[[Sparse matrix]]
**[[Hessenberg matrix]]
**[[Hessian matrix]]
**[[Vandermonde matrix]]
**[[Stochastic matrix]]
**[[Toeplitz matrix]]
***[[Circulant matrix]]
**[[Hankel matrix]]
**[[(0,1)-matrix]]

==Matrix decompositions==
[[Matrix decomposition]]
*[[Cholesky decomposition]]
*[[LU decomposition]]
*[[QR decomposition]]
*[[Polar decomposition]]
*[[Reducing subspace]]
*[[Spectral theorem]]
*[[Singular value decomposition]]
**[[Higher-order singular value decomposition]]
*[[Schur decomposition]]
**[[Schur complement]]
**[[Haynsworth inertia additivity formula]]

==Relations==
*[[Matrix equivalence]]
*[[Matrix congruence]]
*[[Matrix similarity]]
*[[Matrix consimilarity]]
*[[Row equivalence]]

==Computations==
*[[Elementary row operations]]
*[[Householder transformation]]
*[[Least squares]], [[linear least squares (mathematics)|linear least squares]]
*[[Gram–Schmidt process]]
*[[Woodbury matrix identity]]

==Vector spaces==
[[Vector space]]
*[[Linear combination]]
*[[Linear span]]
*[[Linear independence]]
*[[Scalar multiplication]]
*[[Basis (linear algebra)|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]]
**[[Null vector]]
**[[Indefinite orthogonal group]]
* [[Orientation (geometry)]]
**[[Improper rotation]]
* [[Symplectic structure]]

==Multilinear algebra==
[[Multilinear algebra]]
*[[Tensor]]
**[[Classical treatment of tensors]]
**[[Component-free treatment of tensors]]
**[[Gamas's Theorem]]
*[[Outer product]]
*[[Tensor algebra]]
**[[Exterior algebra]]
**[[Symmetric algebra]]
**[[Clifford algebra]]
**[[Geometric algebra]]

==Topics related to affine spaces==
[[Affine space]]
*[[Affine transformation]]
*[[Affine group]]
*[[Affine geometry]]
*[[Affine coordinate system]]
*[[Flat (geometry)]]
*[[Cartesian coordinate system]]
*[[Euclidean group]]
*[[Poincaré group]]
*[[Galilean group]]

==Projective space==
[[Projective space]]
*[[Projective transformation]]
*[[Projective geometry]]
*[[Projective linear group]]
*[[Quadric]] and [[conic section]]

==See also==
*[[Glossary of linear algebra]]
*[[Glossary of tensor theory]]

{{Linear algebra}}

[[Category:Linear algebra|*]]
[[Category:Outlines of mathematics and logic|Linear algebra]]
[[Category:Outlines|Linear algebra]]