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 |
| Published: |
Informa UK Limited,
2020-07-15T21:07:02Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| 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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