Liu, Xiaobo (2023) On the Cross-Shaped Matrices. [MIMS Preprint]
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Abstract
A cross-shaped matrix $X\in\C^{n\times n}$ has nonzero elements located on the main diagonal and the anti-diagonal, so that the sparsity pattern has the shape of a cross. It is shown that $X$ can be factorized into products of identity-plus-rank-two matrices and can be symmetrically permuted to block diagonal form with $2\times 2$ diagonal blocks and, if $n$ is odd, a $1\times 1$ diagonal block. Exploiting these properties we derive explicit formulae for its determinant, inverse, and characteristic polynomial.
| Item Type: | MIMS Preprint |
|---|---|
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory |
| Depositing User: | Xiaobo Liu |
| Date Deposited: | 20 Jan 2023 08:17 |
| Last Modified: | 20 Jan 2023 08:17 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2882 |
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- On the Cross-Shaped Matrices. (deposited 20 Jan 2023 08:17) [Currently Displayed]
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