Special Block Matrix

Asked Mar 17 '19 at 17:29

Active Mar 17 '19 at 18:12

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Let $X,Y\in\mathbb{R}^{n\times n}$ be real square matrices. Let construct the $2n$-by-$2n$ block matrix $$ Z=\begin{bmatrix} X&Y\\ -Y&X \end{bmatrix}. $$ Do the matrices with the block structure of $Z$ have a special name? Does there exist any result on the rank and determinant of these block matrices. This is very similar to Centrosymmetric matrices.

Thanks.

edited Mar 17 '19 at 18:12

Daniele Tampieri

10,752

asked Mar 17 '19 at 17:29

Arthur

1,418

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Regarding the determinant of more general block matrices, the Schur complement may be helpful. – angryavian Mar 17 '19 at 17:31
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You can call these matrices block skey-symmetric. This question gives you an answer about the determinant of these matrices. – Ernie060 Mar 17 '19 at 17:36

Special Block Matrix

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