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|a Strang, W. Gilbert
|e author
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|a Massachusetts Institute of Technology. Department of Mathematics
|e contributor
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|a Multiplying and Factoring Matrices
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|b Informa UK Limited,
|c 2020-07-15T21:07:02Z.
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|z Get fulltext
|u https://hdl.handle.net/1721.1/126212
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|a All of us learn and teach matrix multiplication using rows times columns. Those inner products are the entries of AB. But to go backward-to factor a matrix into triangular or orthogonal or diagonal matrices-outer products are much better. Now AB is the sum of columns of A times rows of B: rank one matrices. Our goal is to produce those columns and rows as simply as possible for A = LU (elimination) and A = CE (echelon form) and A = QR (Gram-Schmidt). Diagonalization by eigenvectors and by singular vectors is also expressed by columns times rows.
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|a Article
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|t 10.1080/00029890.2018.1408378
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|t The American mathematical monthly
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