Nonsingularity of the difference and the sum of two idempotent matrices (Q975612)
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scientific article; zbMATH DE number 5719629
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonsingularity of the difference and the sum of two idempotent matrices |
scientific article; zbMATH DE number 5719629 |
Statements
Nonsingularity of the difference and the sum of two idempotent matrices (English)
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10 June 2010
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It is shown that for any two idempotent matrices \(P, Q\) the nonsingularity of \(P-Q\) is equivalent to the nonsingularity of any combination \(aP+bQ-cPQ\) (\(a, b\neq 0, \;a+b=c\)), and the nonsingularity of \(P+Q\) is equivalent to the nonsingularity of any combination \(aP+bQ-cPQ\) (\(a, b\neq 0,\;a+b\neq c\)).
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idempotent matrix
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direct sum
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rank of matrix
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