A criterion for the existence of common invariant subspaces of matrices (Q1595115)
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scientific article; zbMATH DE number 1559341
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A criterion for the existence of common invariant subspaces of matrices |
scientific article; zbMATH DE number 1559341 |
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A criterion for the existence of common invariant subspaces of matrices (English)
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31 January 2001
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It is shown that square matrices \(A\) and \(B\) have a common invariant subspace \(W\) of dimension \(k\geq 1\) if and only if for some scalar \(s\), \(A+sI\) and \(B+sI\) are invertible and their \(k\)th compounds have a common eigenvector, which is a Grassmann representative for \(W\). The applicability of this criterion and its ability to yield a basis for the common invariant subspace are investigated.
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invariant subspace
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compound matrix
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decomposable vector
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Grassmann space
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