A non-commutative version of Jacobi's equality on the cofactors of a matrix

DOI10.1016/0012-365X(95)00040-4zbMath0864.05071MaRDI QIDQ1815317

Pierre Lalonde

Publication date: 22 June 1997

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

generating functionsdeterminantsinvolutionmatrix inversioncofactorflow monoidJacobi's equalitynon-crossing pathsweighted permutations

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (4)

Hyperbolic Relaxation of $k$-Locally Positive Semidefinite Matrices ⋮ Pfaffians and nonintersecting paths in graphs with cycles: Grassmann algebra methods ⋮ Exact solutions in low-rank approximation with zeros ⋮ Positivity for Gaussian graphical models

Cites Work

• A noncommutative version of the matrix inversion formula
• A combinatorial proof of the Cayley-Hamilton theorem
• Binomial determinants, paths, and hook length formulae
• A combinatorial approach to matrix algebra
• The combinatorial interpretation of the Jacobi identity from Lie algebras
• Combinatorial problems of commutation and rearrangements
• A Combinatorial Proof of Jacobi's Identity
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