Multiplying and Factoring Matrices
Name
mmmf_10.pdf
Description
Accepted version
Size
61.87 KB
Format
Adobe PDF
Checksum (MD5)
ada65c5a691a0abde6e8d6523ece4b68
Author(s)
Strang, W. Gilbert
Date Issued
February 2018
Journal
The American mathematical monthly
Publisher
Informa UK Limited
Citation
Strang, Gilbert. “Multiplying and Factoring Matrices.” The American mathematical monthly, vol. 125, no. 3, 2020, pp. 223-230 © 2020 The Author
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1080/00029890.2018.1408378
