The rank of powers of matrices in a block triangular form (Q1109097)
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scientific article; zbMATH DE number 4069077
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The rank of powers of matrices in a block triangular form |
scientific article; zbMATH DE number 4069077 |
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The rank of powers of matrices in a block triangular form (English)
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1988
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A graph theoretic upper bound for the rank of sufficiently high powers of a complex valued matrix are given. Namely, assuming a lower block triangular form of the matrix, the bound is given in terms of the rank of the powers of its diagonal blocks. An index theorem, which relates the index of the matrix to the indices of its diagonal blocks, is obtained as a corollary.
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graph theoretic methods
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bounds for the rank
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bounds for the index. index theorem
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