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15-xx

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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