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Linear and multilinear algebra; matrix theory
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 also be assigned at least one classification number from Section 01)
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
15A29 Inverse problems
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, 14L24]
15A75 Exterior algebra, Grassmann algebras
15A78 Other algebras built from modules
15A90 Applications of matrix theory to physics
15A99 Miscellaneous topics