Upper and Lower Triangular Matrices | California State University, Northridge - Edubirdie

University:
California State University, Northridge
Course:
MATH 150B | Calculus II
Academic year:

2023
Views:

335

Pages:

1
Author:

Andrew M.

Upper and Lower Triangular Matrices A quare (non) matrix Cis UT -Upper Triangular (UT) FE CID for j ) the diagonal lements are all equal tرا به we have a upper-unit triangular (UUT) Lower Trianguin (LT) ife C. O for icj (if the diagonal elements are all equal tol. we have a lower-unt triangular (LUT) matix) - Diagonal (0) if co for itj - ODD 20 LIT 120 Theorem. The product of the two UT (WT)matrices is UT (OUT) • The product of the two LT (WT) matrices is LT (LUT) • The product of the two D matrices is D 6. Why are we interested in these matrices? Suppore Ayd, cwhere A is LT (with non-zero diagon-1 term). Then, the solutions are recursive (forwoud substitution) Example xd. Simitaly, suppar Axed, where A is UT (with non-Zerd diagonal terms). Then, the solution are recursive (backward substitu Example:

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