Multiplying and Factoring Matrices
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 m...
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| Format: | Article |
| Language: | English |
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Informa UK Limited
2020
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| Online Access: | https://hdl.handle.net/1721.1/126212 |
| Summary: | 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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