How to establish universal block-matrix factorizations (Q2736392)
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scientific article; zbMATH DE number 1638697
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | How to establish universal block-matrix factorizations |
scientific article; zbMATH DE number 1638697 |
Statements
How to establish universal block-matrix factorizations (English)
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29 August 2001
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universal factorization
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block matrix
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quaternion matrix
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involutory matrix
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idempotent matrix
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similarity factorization
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quaternion algebra
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Clifford algebras
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A general and simple method for establishing universal factorizations of block matrices is presented. The case of \(2 \times 2\) and \(4 \times 4\) matrices is illustrated by useful expressions of factorization equalities. These equalities are used to reveal the relationship between real quaternion matrices and real block matrices. The universal similarity factorization equality is also applied to a linear combination of involutory matrices, to idempotent matrices and can be extended to a generalized quaternion algebra and to all \(2^n\)-dimensional Clifford algebras.
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