Inversion of the Multiplicative Matrix Compound Operator
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914606684831744 |
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| author | Dey, Debojyoti Ofir, Ron Grussler, Christian |
| author_facet | Dey, Debojyoti Ofir, Ron Grussler, Christian |
| contents | We study the problem of determining a matrix whose $k$th multiplicative compound 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27682 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inversion of the Multiplicative Matrix Compound Operator Dey, Debojyoti Ofir, Ron Grussler, Christian Rings and Algebras Numerical Analysis Systems and Control Algebraic Geometry 15A29, 15A69, 15A75 We study the problem of determining a matrix whose $k$th multiplicative compound 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. |
| title | Inversion of the Multiplicative Matrix Compound Operator |
| topic | Rings and Algebras Numerical Analysis Systems and Control Algebraic Geometry 15A29, 15A69, 15A75 |
| url | https://arxiv.org/abs/2605.27682 |