# Activities / Library

## Mathematical Sciences Classification System

### 15Axx - Basic linear algebra

• 15A03
Vector spaces, linear dependence, rank
• 15A04
Linear transformations, semilinear transformations
• 15A06
Linear equations
• 15A09
Matrix inversion, generalized inverses
• 15A12
• 15A15
• 15A16
Matrix exponential and similar functions of matrices
• 15A18
Eigenvalues, singular values, and eigenvectors
• 15A21
Canonical forms, reductions, classification
• 15A22
• 15A23
Factorization of matrices
• 15A24
Matrix equations and identities
• 15A27
Commutativity
• 15A29
Inverse problems
• 15A30
• 15A33
Matrices over special rings (quaternions, finite fields, etc.)
• 15A36
Matrices of integers
• 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
• 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
• 15A90
Applications of matrix theory to physics
• 15A99
Miscellaneous topics