MSC2020 · 15Axx

Basic linear algebra

6 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

15A03Vector spaces, linear dependence, rank, lineability0 15A04Linear transformations, semilinear transformations0 15A06Linear equations (linear algebraic aspects)0 15A09Theory of matrix inversion and generalized inverses0 15A10Applications of generalized inverses0 15A12Conditioning of matrices0 15A15Determinants, permanents, traces, other special matrix functions0 15A16Matrix exponential and similar functions of matrices0 15A18Eigenvalues, singular values, and eigenvectors0 15A20Diagonalization, Jordan forms0 15A21Canonical forms, reductions, classification0 15A22Matrix pencils0 15A23Factorization of matrices0 15A24Matrix equations and identities0 15A27Commutativity of matrices0 15A29Inverse problems in linear algebra0 15A30Algebraic systems of matrices0 15A39Linear inequalities of matrices0 15A42Inequalities involving eigenvalues and eigenvectors0 15A45Miscellaneous inequalities involving matrices1 15A54Matrices over function rings in one or more variables0 15A60Norms of matrices, numerical range, applications of functional analysis to matrix theory2 15A63Quadratic and bilinear forms, inner products0 15A66Clifford algebras, spinors0 15A67Applications of Clifford algebras to physics, etc.0 15A69Multilinear algebra, tensor calculus3 15A72Vector and tensor algebra, theory of invariants0 15A75Exterior algebra, Grassmann algebras0 15A78Other algebras built from modules0 15A80Max-plus and related algebras0 15A83Matrix completion problems0 15A86Linear preserver problems0 15A99Basic linear algebra0

Mapped problems

OP-12147AlgebraStatus unassessed

Matrix multiplications and AM-GM inequalities (AlphaEvolve problem 47)

Matrix multiplications and AM-GM inequalities (AlphaEvolve problem 47). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12127AnalysisStatus unassessed

Crouzeix's Conjecture (AlphaEvolve problem 25)

Crouzeix's Conjecture (AlphaEvolve problem 25). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12018Computational complexityOpen

Dual matrix multiplication exponent ( $C_{15b}$ )

Dual matrix multiplication exponent: determine C 15b or improve its bounds; the repository records 0.321334 (lower) and 1 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12017Computational complexityOpen

Matrix multiplication exponent ( $C_{15a}$ )

Matrix multiplication exponent: determine C 15a or improve its bounds; the repository records 2 (lower) and 2.371177 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-11993AnalysisSolved

Crouzeix constant ( $C_{2}$ )

Crouzeix constant: determine C 2 or improve its bounds; the repository records 2 (lower) and 2 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-11970AlgebraOpen

The Rank of the $4\times4$ Matrix-Multiplication Tensor

The Rank of the 4 times4 Matrix-Multiplication Tensor. Moderately interesting problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026