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- W1995759580 abstract "For some years it has been known that every singular square matrix over an arbitrary field F is a product of idempotent matrices over F . This paper quantifies that result to some extent. Main result: for every field F and every pair ( n , k ) of positive integers, an n × n matrix S over F is a product of k idempotent matrices over F iff rank( I − S )⩽ k · nullity S . The proof of the “if” part involves only elementary matrix operations and may thus be regarded as constructive. Corollary: (for every field F and every positive integer n ) each singular n × n matrix over F is a product of n idempotent matrices over F , and there is a singular n × n matrix over F which is not a product of n − 1 idempotent matrices." @default.
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- W1995759580 date "1978-01-01" @default.
- W1995759580 modified "2023-09-28" @default.
- W1995759580 title "Products of idempotent matrices" @default.
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- W1995759580 doi "https://doi.org/10.1016/0024-3795(78)90006-x" @default.
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