Liu, Xiaobo (2023) On the CrossShaped Matrices. [MIMS Preprint]
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Abstract
A crossshaped matrix $X\in\C^{n\times n}$ has nonzero elements located on the main diagonal and the antidiagonal, so that the sparsity pattern has the shape of a cross. It is shown that $X$ can be factorized into products of identityplusranktwo 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 09:37 
Last Modified:  20 Jan 2023 09:37 
URI:  https://eprints.maths.manchester.ac.uk/id/eprint/2883 
Available Versions of this Item

On the CrossShaped Matrices. (deposited 20 Jan 2023 08:17)
 On the CrossShaped Matrices. (deposited 20 Jan 2023 09:37) [Currently Displayed]
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