## 15Axx Basic linear algebra

- 15A03 Vector spaces, linear dependence, rank (1)
- 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]
- 15A16 Matrix exponential and similar functions of matrices
- 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.)
- 15A39 Linear inequalities
- 15A42 Inequalities involving eigenvalues and eigenvectors
- 15A45 Miscellaneous inequalities involving matrices
- 15A54 Matrices over function rings in one or more variables
- 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
- 15A80 Max-plus and related algebras
- 15A83 Matrix completion problems
- 15A86 Linear preserver problems
- 15A99 Miscellaneous topics