The bialternate matrix product revisited. (English) Zbl 1211.15009

Over the years, the bialternate matrix product, introduced by C. Stépanos [Journ. de Math. (5) 6, 73–128 (1900; JFM 31.0132.01)], was used as an efficient tool in stability theory, especially in studying polynomial and matrix stability and in the theory of dynamical systems in detecting and computing Hopf bifurcations in systems of ordinary differential equations.
In this paper, the bialternate product of two square matrices is re-examined together with another matrix product defined by means of the permanent function and having similar properties. The authors present old and new results concerning both products in a unified manner. A simple and elegant relation with the Kronecker product of matrices is also given.


15A15 Determinants, permanents, traces, other special matrix functions
15A18 Eigenvalues, singular values, and eigenvectors
15A69 Multilinear algebra, tensor calculus


JFM 31.0132.01
Full Text: DOI


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