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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.18928 |
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| _version_ | 1866915634976129024 |
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| author | Homolya, Szilvia Szigeti, Jenő |
| author_facet | Homolya, Szilvia Szigeti, Jenő |
| contents | An nxn matrix A over an arbitrary unitary ring R satisfies invariant left and right Cayley-Hamilton identities with matrix coefficients C(i), D(i) having commutator sum entries. If R has a grading similar to the case of Grassmann algebras, then we prove that C(i)-D(i)-AC(i+1)+D(i+1)A=-2p(i+1)A1 for all i, where A1 and p(i+1) are the odd components of A and of the symmetric characteristic polynomial of A, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the left and right coefficients of the general Cayley-Hamilton identities for an nxn matrix Homolya, Szilvia Szigeti, Jenő Rings and Algebras An nxn matrix A over an arbitrary unitary ring R satisfies invariant left and right Cayley-Hamilton identities with matrix coefficients C(i), D(i) having commutator sum entries. If R has a grading similar to the case of Grassmann algebras, then we prove that C(i)-D(i)-AC(i+1)+D(i+1)A=-2p(i+1)A1 for all i, where A1 and p(i+1) are the odd components of A and of the symmetric characteristic polynomial of A, respectively. |
| title | On the left and right coefficients of the general Cayley-Hamilton identities for an nxn matrix |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2511.18928 |