Chapter 1.6 SpecialMatrices

# Outline diagonal matrices triangular matrices

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: )T = (AT )−1 = A−1 . Outline Diagonal Matrices Triangular Matrices Symmetric Matrices Symmetric Products Theorem Suppose A = [aij ] is an m × n matrix. (a) AAT and AT A are symmetric matrices. (b) If A is invertible, then AAT and AT A are invertible. Proof. (a) (AAT )T = (AT )T AT = AAT and (AT A)T = AT (AT )T = AT A. (b) Since A is invertible, so is AT and therefore so are the products AAT and AT A. Outline Diagonal Matrices Triangular Matrices Example Example Demonstrate the Theorem using 1 2 −3 −4 2 A = 0 1 −1 −1 0 1 3 Symmetric Matrices...
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