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
  • 8
    15A69
    Multilinear algebra, tensor products
  • 16
    15A72
    Vector and tensor algebra, theory of invariants [See also 13A50, 14L24]
  • 10
    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

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