### 15-XX Linear and multilinear algebra; matrix theory

{(finite and infinite)}
- 15-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 15-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 15-02 Research exposition (monographs, survey articles)
- 15-03 Historical (must be assigned at least one classification number from 01-XX)
- 15-04 Explicit machine computation and programs (not the theory of computation or programming)
- 15-06 Proceedings, conferences, collections, etc.
- 15A03 Vector spaces, linear dependence, rank
- 15A04 Linear transformations, semilinear transformations
- 15A06 Linear equations
- 15A09 Matrix inversion, generalized inverses
- 15A12 Conditioning of matrices, See also {65F35}
- 15A15 Determinants, permanents, other special matrix functions, See also {19B10, 19B14}
- 15A18 Eigenvalues, singular values, and eigenvectors
- 15A21 Canonical forms, reductions, classification
- 15A22 Matrix pencils, See also {47A56}
- 15A23 Factorization of matrices
- 15A24 Matrix equations and identities
- 15A27 Commutativity
- 15A30 Algebraic systems of matrices, See also {16S50, 20Gxx,
20Hxx}
- 15A33 Matrices over special rings (quaternions, finite fields, etc.)
- 15A36 Matrices of integers, See also {11C20}
- 15A39 Linear inequalities
- 15A42 Inequalities involving eigenvalues and eigenvectors
- 15A45 Miscellaneous inequalities involving matrices
- 15A48 Positive matrices and their generalizations; cones of matrices
- 15A51 Stochastic matrices
- 15A52 Random matrices
- 15A54 Matrices over function rings in one or more variables
- 15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)
- 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory, See also {65F35,
65J05}
- 15A63 Quadratic and bilinear forms, inner products See mainly{
11Exx}
- 15A66 Clifford algebras, spinors
- 15A69 Multilinear algebra, tensor products
- 15A72 Vector and tensor algebra, theory of invariants, See Also {13A50, 14D25}
- 15A75 Exterior algebra, Grassmann algebras
- 15A78 Other algebras built from modules
- 15A90 Applications of matrix theory to physics
- 15A99 Miscellaneous topics

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