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Preprint
On the principal minors of the powers of a matrix
arXiv (Cornell University)
16 Apr 2022
Abstract
Gazeta Matematica, Seria A, Anul XL (CXIX), nr. 1--2, 2022 We show that if $A$ is an $n\times n$-matrix, then the diagonal entries of
each power $A^{m}$ are uniquely determined by the principal minors of $A$, and
can be written as universal (integral) polynomials in the latter. Furthermore,
if the latter all equal $1$, then so do the former. These results are inspired
by Problem B5 on the Putnam contest 2021, and shed a new light on the behavior
of minors under matrix multiplication.
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Details
- Title
- On the principal minors of the powers of a matrix
- Creators
- Darij Grinberg
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862238704721