Properties of a unitary matrix obtained from a sequence of normalized vectors (Q2923357)
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scientific article; zbMATH DE number 6356184
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Properties of a unitary matrix obtained from a sequence of normalized vectors |
scientific article; zbMATH DE number 6356184 |
Statements
15 October 2014
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orthogonality
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augmented orthogonal matrix
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singular value decomposition
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CS decomposition
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rank deficiency
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product of projectors
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Properties of a unitary matrix obtained from a sequence of normalized vectors (English)
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The authors consider the problem of forming an \((n+k) \times (n+k)\) unitary matrix from a sequence of \(k\) unitary \(n\)-dimensional complex vectors, \(V_k = [v_1, \dots, v_k]\). A key component of the analysis is the \(k \times k\) strictly upper triangular matrix \(S_k\) arising from \(V_k\). The results obtained are applied to general Euclidean norm vectors, and to symmetric Lanczos process.
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