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Outline of linear algebra
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<h2 id="linear-equations">Linear equations</h2> <p><a href="/facts/Linear_equation/JfCgALwf">Linear equation</a> </p> <ul><li><a href="/facts/System_of_linear_equations/fk9CFdgp">System of linear equations</a></li> <li><a href="/facts/Determinant/eGYqJ2TF">Determinant</a> <ul><li><a href="/facts/Minor_(linear_algebra)/CMudF5Eh">Minor</a></li> <li><a href="/facts/Cauchy%25E2%2580%2593Binet_formula/jbRCH0tj">Cauchy–Binet formula</a></li></ul></li> <li><a href="/facts/Cramer%2527s_rule/aUt4Cena">Cramer's rule</a></li> <li><a href="/facts/Gaussian_elimination/23Rvf4ht">Gaussian elimination</a></li> <li><a href="/facts/Gauss%25E2%2580%2593Jordan_elimination/23Rvf4ht">Gauss–Jordan elimination</a></li> <li><a href="/facts/Overcompleteness/th2TMz0o">Overcompleteness</a></li> <li><a href="/facts/Strassen_algorithm/rrIGRSNp">Strassen algorithm</a></li></ul> <h2 id="matrices">Matrices</h2> <p><a href="/facts/Matrix_(mathematics)/qa8FI4ko">Matrix</a> </p> <ul><li><a href="/facts/Matrix_addition/6zzLWyL0">Matrix addition</a></li> <li><a href="/facts/Matrix_multiplication/lYDB6Ro2">Matrix multiplication</a></li> <li><a href="/facts/Basis_transformation_matrix/TEcLqS40">Basis transformation matrix</a></li> <li><a href="/facts/Characteristic_polynomial/7m8roDqo">Characteristic polynomial</a></li> <li><a href="/facts/Trace_(matrix)/dchFFvHt">Trace</a></li> <li><a href="/facts/Eigenvalue%2c_eigenvector_and_eigenspace/8TjEoT8u">Eigenvalue, eigenvector and eigenspace</a> <ul><li><a href="/facts/Cayley%25E2%2580%2593Hamilton_theorem/pXdJXWkR">Cayley–Hamilton theorem</a></li> <li><a href="/facts/Spread_of_a_matrix/6NvmV42N">Spread of a matrix</a></li> <li><a href="/facts/Jordan_normal_form/M7ezYbnl">Jordan normal form</a></li> <li><a href="/facts/Weyr_canonical_form/W1BGVQjy">Weyr canonical form</a></li></ul></li> <li><a href="/facts/Rank_(matrix_theory)/Yp9b5LK3">Rank</a></li> <li><a href="/facts/Matrix_inversion/fPqXk3V8">Matrix inversion</a>, <a href="/facts/Invertible_matrix/fPqXk3V8">invertible matrix</a> <ul><li><a href="/facts/Pseudoinverse/4xVKDIAp">Pseudoinverse</a></li></ul></li> <li><a href="/facts/Adjugate/jjT9v8ox">Adjugate</a></li> <li><a href="/facts/Transpose/8wmsagGS">Transpose</a> <ul><li><a href="/facts/Dot_product/tNz8MLjT">Dot product</a></li> <li><a href="/facts/Symmetric_matrix/08CGwjNl">Symmetric matrix</a></li> <li><a href="/facts/Orthogonal_matrix/WDXBXYB5">Orthogonal matrix</a></li> <li><a href="/facts/Skew-symmetric_matrix/nw5CQeLN">Skew-symmetric matrix</a></li> <li><a href="/facts/Conjugate_transpose/7eBWtqVG">Conjugate transpose</a> <ul><li><a href="/facts/Unitary_matrix/8fsxv3KD">Unitary matrix</a></li> <li><a href="/facts/Hermitian_matrix/qArPblYo">Hermitian matrix</a>, <a href="/facts/Antihermitian_matrix/wxjjnvCC">Antihermitian matrix</a></li></ul></li></ul></li> <li><a href="/facts/Positive-definite_matrix/Hbr6AuPS">Positive-definite</a>, <a href="/facts/Positive-semidefinite_matrix/Hbr6AuPS">positive-semidefinite matrix</a></li> <li><a href="/facts/Pfaffian/3CmddqLu">Pfaffian</a></li> <li><a href="/facts/Projection_(linear_algebra)/sElXGkxD">Projection</a></li> <li><a href="/facts/Spectral_theorem/Vqc04B21">Spectral theorem</a></li> <li><a href="/facts/Perron%25E2%2580%2593Frobenius_theorem/K9nDY7DL">Perron–Frobenius theorem</a></li> <li><a href="/facts/List_of_matrices/op20J9jC">List of matrices</a> <ul><li><a href="/facts/Diagonal_matrix/tjIAHrE6">Diagonal matrix</a>, <a href="/facts/Main_diagonal/rkT2F08Q">main diagonal</a> <ul><li><a href="/facts/Diagonalizable_matrix/y3MkyTCy">Diagonalizable matrix</a></li></ul></li> <li><a href="/facts/Triangular_matrix/qjXSFMM3">Triangular matrix</a></li> <li><a href="/facts/Tridiagonal_matrix/1SK5A0rP">Tridiagonal matrix</a></li> <li><a href="/facts/Block_matrix/fPI8HX9f">Block matrix</a></li> <li><a href="/facts/Sparse_matrix/FFtN0XjR">Sparse matrix</a></li> <li><a href="/facts/Hessenberg_matrix/vy7p7s3Y">Hessenberg matrix</a></li> <li><a href="/facts/Hessian_matrix/RguMNr3m">Hessian matrix</a></li> <li><a href="/facts/Vandermonde_matrix/8oSbUk6u">Vandermonde matrix</a></li> <li><a href="/facts/Stochastic_matrix/2cRWAqC3">Stochastic matrix</a></li> <li><a href="/facts/Toeplitz_matrix/WAjSdlaW">Toeplitz matrix</a> <ul><li><a href="/facts/Circulant_matrix/71ohEKT2">Circulant matrix</a></li></ul></li> <li><a href="/facts/Hankel_matrix/96ePFS7m">Hankel matrix</a></li> <li><a href="/facts/(0%2c1)-matrix/pS4BnBzj">(0,1)-matrix</a></li></ul></li></ul> <h2 id="matrix-decompositions">Matrix decompositions</h2> <p><a href="/facts/Matrix_decomposition/xVBnAg0x">Matrix decomposition</a> </p> <ul><li><a href="/facts/Cholesky_decomposition/Q3IjkuTs">Cholesky decomposition</a></li> <li><a href="/facts/LU_decomposition/M13Ew8RD">LU decomposition</a></li> <li><a href="/facts/QR_decomposition/NswfKLGY">QR decomposition</a></li> <li><a href="/facts/Polar_decomposition/XWQLdp9B">Polar decomposition</a></li> <li><a href="/facts/Reducing_subspace/3h7uMgqb">Reducing subspace</a></li> <li><a href="/facts/Spectral_theorem/Vqc04B21">Spectral theorem</a></li> <li><a href="/facts/Singular_value_decomposition/8t3v6wk3">Singular value decomposition</a> <ul><li><a href="/facts/Higher-order_singular_value_decomposition/JTtTDy39">Higher-order singular value decomposition</a></li></ul></li> <li><a href="/facts/Schur_decomposition/EYNrqHmh">Schur decomposition</a> <ul><li><a href="/facts/Schur_complement/n5Frtl3p">Schur complement</a></li> <li><a href="/facts/Haynsworth_inertia_additivity_formula/x71a5V9k">Haynsworth inertia additivity formula</a></li></ul></li></ul> <h2 id="relations">Relations</h2> <ul><li><a href="/facts/Matrix_equivalence/cGDWP8gY">Matrix equivalence</a></li> <li><a href="/facts/Matrix_congruence/L5nPV4BQ">Matrix congruence</a></li> <li><a href="/facts/Matrix_similarity/ySevpav1">Matrix similarity</a></li> <li><a href="/facts/Matrix_consimilarity/oLAg7VdF">Matrix consimilarity</a></li> <li><a href="/facts/Row_equivalence/UEhrr5gE">Row equivalence</a></li></ul> <h2 id="computations">Computations</h2> <ul><li><a href="/facts/Elementary_row_operations/coFCElwg">Elementary row operations</a></li> <li><a href="/facts/Householder_transformation/1L87qsqE">Householder transformation</a></li> <li><a href="/facts/Least_squares/50jIwbxC">Least squares</a>, <a href="/facts/Linear_least_squares_(mathematics)/dKctFUCV">linear least squares</a></li> <li><a href="/facts/Gram%25E2%2580%2593Schmidt_process/vRNpld3t">Gram–Schmidt process</a></li> <li><a href="/facts/Woodbury_matrix_identity/bcmjY73W">Woodbury matrix identity</a></li></ul> <h2 id="vector-spaces">Vector spaces</h2> <p><a href="/facts/Vector_space/M1pxMLx2">Vector space</a> </p> <ul><li><a href="/facts/Linear_combination/CVjL6kuN">Linear combination</a></li> <li><a href="/facts/Linear_span/vPjclEtb">Linear span</a></li> <li><a href="/facts/Linear_independence/8JrHfIIa">Linear independence</a></li> <li><a href="/facts/Scalar_multiplication/jroFDfbM">Scalar multiplication</a></li> <li><a href="/facts/Basis_(linear_algebra)/89IPoN6c">Basis</a> <ul><li><a href="/facts/Change_of_basis/Hnu1Spcc">Change of basis</a></li> <li><a href="/facts/Hamel_basis/89IPoN6c">Hamel basis</a></li></ul></li> <li><a href="/facts/Cyclic_decomposition_theorem/DbBecYez">Cyclic decomposition theorem</a></li> <li><a href="/facts/Dimension_theorem_for_vector_spaces/1dQJF9fT">Dimension theorem for vector spaces</a> <ul><li><a href="/facts/Hamel_dimension/z8m02A3W">Hamel dimension</a></li></ul></li> <li><a href="/facts/Examples_of_vector_spaces/tNTbVppn">Examples of vector spaces</a></li> <li><a href="/facts/Linear_map/Q1PBKNVV">Linear map</a> <ul><li><a href="/facts/Shear_mapping/HVCYblfU">Shear mapping</a> or <a href="/facts/Galilean_transformation/CR8VWxbr">Galilean transformation</a></li> <li><a href="/facts/Squeeze_mapping/CYxzaaKR">Squeeze mapping</a> or <a href="/facts/Lorentz_transformation/jotJL06G">Lorentz transformation</a></li></ul></li> <li><a href="/facts/Linear_subspace/2wtKTgHL">Linear subspace</a> <ul><li><a href="/facts/Row_and_column_spaces/INXbQVNI">Row and column spaces</a></li> <li><a href="/facts/Column_space/INXbQVNI">Column space</a></li> <li><a href="/facts/Row_space/INXbQVNI">Row space</a></li> <li><a href="/facts/Cyclic_subspace/DbBecYez">Cyclic subspace</a></li> <li><a href="/facts/Null_space/adhGUYa0">Null space</a>, nullity</li> <li><a href="/facts/Rank%25E2%2580%2593nullity_theorem/3wN4gcJu">Rank–nullity theorem</a></li> <li><a href="/facts/Nullity_theorem/Hl1jNHRH">Nullity theorem</a></li></ul></li> <li><a href="/facts/Dual_space/4Uw4Knz1">Dual space</a> <ul><li><a href="/facts/Linear_function/Ejvy8CKy">Linear function</a></li> <li><a href="/facts/Linear_functional/oGh7Asrz">Linear functional</a></li></ul></li> <li><a href="/facts/Category_of_vector_spaces/AnnF9JKf">Category of vector spaces</a></li></ul> <h2 id="structures">Structures</h2> <ul><li><a href="/facts/Topological_vector_space/XRex1ChN">Topological vector space</a></li> <li><a href="/facts/Normed_vector_space/rmDljfyE">Normed vector space</a></li> <li><a href="/facts/Inner_product_space/HoyjElEy">Inner product space</a> <ul><li><a href="/facts/Euclidean_space/R2UbzmzM">Euclidean space</a></li> <li><a href="/facts/Orthogonality/JVIjYPog">Orthogonality</a></li> <li><a href="/facts/Orthogonal_complement/a13oQBsz">Orthogonal complement</a></li> <li><a href="/facts/Orthogonal_projection/sElXGkxD">Orthogonal projection</a></li> <li><a href="/facts/Orthogonal_group/jKWM1KDM">Orthogonal group</a></li></ul></li> <li><a href="/facts/Pseudo-Euclidean_space/UW6sbGeK">Pseudo-Euclidean space</a> <ul><li><a href="/facts/Null_vector/sjkdQtdS">Null vector</a></li> <li><a href="/facts/Indefinite_orthogonal_group/snKhwDB2">Indefinite orthogonal group</a></li></ul></li> <li><a href="/facts/Orientation_(geometry)/Tj24mTJ8">Orientation (geometry)</a> <ul><li><a href="/facts/Improper_rotation/kcLdCD9r">Improper rotation</a></li></ul></li> <li><a href="/facts/Symplectic_structure/runXFCea">Symplectic structure</a></li></ul> <h2 id="multilinear-algebra">Multilinear algebra</h2> <p><a href="/facts/Multilinear_algebra/LrwpUFsM">Multilinear algebra</a> </p> <ul><li><a href="/facts/Tensor/pNjFo5tV">Tensor</a> <ul><li><a href="/facts/Classical_treatment_of_tensors/pNjFo5tV">Classical treatment of tensors</a></li> <li><a href="/facts/Component-free_treatment_of_tensors/2KuNm0MK">Component-free treatment of tensors</a></li> <li><a href="/facts/Gamas%2527s_Theorem/GWVLhML1">Gamas's Theorem</a></li></ul></li> <li><a href="/facts/Outer_product/qR9C2BU1">Outer product</a></li> <li><a href="/facts/Tensor_algebra/H7CKKryf">Tensor algebra</a> <ul><li><a href="/facts/Exterior_algebra/rdN4TvpR">Exterior algebra</a></li> <li><a href="/facts/Symmetric_algebra/A8FthY0N">Symmetric algebra</a></li> <li><a href="/facts/Clifford_algebra/qnqSCz5h">Clifford algebra</a></li> <li><a href="/facts/Geometric_algebra/yykKMNYx">Geometric algebra</a></li></ul></li></ul> <h2 id="topics-related-to-affine-spaces">Topics related to affine spaces</h2> <p><a href="/facts/Affine_space/tlvI3oX1">Affine space</a> </p> <ul><li><a href="/facts/Affine_transformation/BD7yDr10">Affine transformation</a></li> <li><a href="/facts/Affine_group/pe8CxKXV">Affine group</a></li> <li><a href="/facts/Affine_geometry/yUGgTx2n">Affine geometry</a></li> <li><a href="/facts/Affine_coordinate_system/tlvI3oX1">Affine coordinate system</a></li> <li><a href="/facts/Flat_(geometry)/IlMjx7RK">Flat (geometry)</a></li> <li><a href="/facts/Cartesian_coordinate_system/lkTqvMmB">Cartesian coordinate system</a></li> <li><a href="/facts/Euclidean_group/VdTSdwzl">Euclidean group</a></li> <li><a href="/facts/Poincar%25C3%25A9_group/3IerRYG1">Poincaré group</a></li> <li><a href="/facts/Galilean_group/CR8VWxbr">Galilean group</a></li></ul> <h2 id="projective-space">Projective space</h2> <p><a href="/facts/Projective_space/7MSpA9cM">Projective space</a> </p> <ul><li><a href="/facts/Projective_transformation/wCkNzUjd">Projective transformation</a></li> <li><a href="/facts/Projective_geometry/rHKSaEbx">Projective geometry</a></li> <li><a href="/facts/Projective_linear_group/y7P9rMyR">Projective linear group</a></li> <li><a href="/facts/Quadric/L3cTApd4">Quadric</a> and <a href="/facts/Conic_section/teqgLptX">conic section</a></li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Glossary_of_linear_algebra/e68U5egp">Glossary of linear algebra</a></li> <li><a href="/facts/Glossary_of_tensor_theory/QL2GnCmr">Glossary of tensor theory</a></li></ul>