Chapter 1.6 SpecialMatrices

# ann b a is invertible if and only if aii 0 for

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s invertible if and only if aii = 0 for all i, and in this case − − − A−r = diag{a11r , a22r , . . . , annr }. In particular, products and inverses of diagonal matrices are diagonal. Proof. Induction. Outline Diagonal Matrices Triangular Matrices Symmetric Matrices Products with Diagonal Matrices Theorem Suppose A = diag{d1 , d2 , . . . , dn }. (a) If B is an n × m matrix with row vectors w1 , w2 , . . . , wn , then d1 w1 d2 w2 AB = . . . dn wn (b) If B is an m × n matrix with column vectors v1 , v2 , . . . , vn , then BA = d1 v1 d2 v2 · · · dn vn Outline Diagonal Matrices Triangular Matrices Symmetric Matrices Examples Example 1 2 3 Discuss the invertibility of the diagonal 1 0 0 0 , B = A = 0 −2 0 0 −3 matrices 1 0 0 0 0 0 0 0 0 0 0 0 5 0 0 −2 Find B 2 , A−1 , and A−3 for A and B in Example 1. Demonstrate the pr...
View Full Document

## This note was uploaded on 02/10/2014 for the course MATH 2270 taught by Professor Kenyonj.platt during the Spring '14 term at Snow College.

Ask a homework question - tutors are online