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Mathematical Sciences Classification System

15Axx - Basic linear algebra

• 2
  15A03
  Vector spaces, linear dependence, rank
• 2
  15A04
  Linear transformations, semilinear transformations
• 3
  15A06
  Linear equations
• 9
  15A09
  Matrix inversion, generalized inverses
• 1
  15A12
  Conditioning of matrices [See also 65F35]
• 6
  15A15
  Determinants, permanents, other special matrix functions [See also 19B10, 19B14]
• 3
  15A16
  Matrix exponential and similar functions of matrices
• 37
  15A18
  Eigenvalues, singular values, and eigenvectors
• 19
  15A21
  Canonical forms, reductions, classification
• 15A22
  Matrix pencils [See also 47A56]
• 7
  15A23
  Factorization of matrices
• 8
  15A24
  Matrix equations and identities
• 2
  15A27
  Commutativity
• 1
  15A29
  Inverse problems
• 6
  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]
• 2
  15A39
  Linear inequalities
• 8
  15A42
  Inequalities involving eigenvalues and eigenvectors
• 10
  15A45
  Miscellaneous inequalities involving matrices
• 15A48
  Positive matrices and their generalizations; cones of matrices
• 15A51
  Stochastic matrices
• 15A52
  Random matrices
• 1
  15A54
  Matrices over function rings in one or more variables
• 15A57
  Other types of matrices (Hermitian, skew-Hermitian, etc.)
• 9
  15A60
  Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
• 7
  15A63
  Quadratic and bilinear forms, inner products [See mainly 11Exx]
• 30
  15A66
  Clifford algebras, spinors
• 10
  15A69
  Multilinear algebra, tensor products
• 16
  15A72
  Vector and tensor algebra, theory of invariants [See also 13A50, 14L24]
• 11
  15A75
  Exterior algebra, Grassmann algebras
• 15A78
  Other algebras built from modules
• 4
  15A80
  Max-plus and related algebras
• 3
  15A83
  Matrix completion problems
• 15A86
  Linear preserver problems
• 4
  15A90
  Applications of matrix theory to physics
• 3
  15A99
  Miscellaneous topics