Anti-diagonalization theory and algorithm of matrices—from skew-symmetric matrices to arbitrary matrices

In this paper, a novel algorithm for anti-diagonalization of skew symmetric matrices via using orthogonal similarity transformations has been introduced. The theory and algorithm about the anti-triangular factorization of skew-symmetric matrices are proved. In the case of skew-symmetric matrices, we...

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Bibliographic Details
Published in:	Mathematics and computers in simulation Vol. 209; pp. 44 - 54
Main Authors:	Wu, Yunyun, Li, Yayun
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.07.2023
Subjects:	Anti-diagonal form Double eigenvector system Skew-symmetric matrices Skew-symmetric matrices Double eigenvector system Anti-diagonal form
ISSN:	0378-4754
Online Access:	Get full text
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Summary:	In this paper, a novel algorithm for anti-diagonalization of skew symmetric matrices via using orthogonal similarity transformations has been introduced. The theory and algorithm about the anti-triangular factorization of skew-symmetric matrices are proved. In the case of skew-symmetric matrices, we prove that the anti-diagonal form is always obtained, resulting in developing a new factorization scheme. Moreover, a theoretical algorithm is given based on the theory of double eigenvector system, which provides all the information for the factorization of arbitrary matrices. Finally, the proposed algorithm is verified effective and efficient through the numerical experiments of anti-diagonalization of matrices over a general number field.
ISSN:	0378-4754
DOI:	10.1016/j.matcom.2023.01.045