Preprint
The trace Cayley-Hamilton theorem
ArXiv.org
23 Oct 2025
Abstract
In this expository paper, various properties of matrix traces, determinants and adjugate matrices are proved, including the *trace Cayley-Hamilton theorem*, which says that \[ kc_k + _i=1^k Tr (A^i) c_k-i = 0 for every kınN \] whenever$A$is an$n\times n$ -matrix with characteristic polynomial$\det (tI_n - A) = \sum_{i=0}^n c_{n-i} t^i$over a commutative ring$\mathbb{K}$ . While the results are not new, some of the proofs are. The proofs illustrate some general techniques in linear algebra over commutative rings.
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Details
- Title
- The trace Cayley-Hamilton theorem
- Creators
- Darij Grinberg - Drexel University
- Publication Details
- ArXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022127752304721