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arXiv · 2605.27682

Inversion of the Multiplicative Matrix Compound Operator

Debojyoti Dey·Ron Ofir·Christian Grussler
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Abstract

We study the problem of determining a matrix whose $k$th multiplicative compound, with $k > 1$, is a prescribed matrix $M$. The cardinality of the set of matrices whose $k$th multiplicative compound equals $M$ is characterized in terms of $\rank(M)$. On the one hand, if $\rank(M)\le 1$, it is shown that there exist infinitely many such matrices for which a complete characterization is determined. On the other hand, if $\rank(M)>1$, then there exists a unique matrix -- up to an overall sign -- whose compound is $M$. An algorithm for finding a matrix whose compound equals $M$ is detailed, and its time complexity is analyzed.

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Debojyoti Dey, Ron Ofir, Christian Grussler. 2026-05-26. Inversion of the Multiplicative Matrix Compound Operator. https://arxiv.org/abs/2605.27682

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