554-HW-7q - 7 Let T be the linear operator on R 4 which is...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 7 Let T be the linear operator on R 4 which is represented in the standard ordered basis by the matrix M = 0 0 0 a 0 0 0 b 0 0 c Under what conditions on a,b,c is T diagonalizable? 7 Let T be a linear operator on the n-dimensional vector space V , and suppose that T has n distinct characteristic values. Prove that T is diagonalizable. 7 Let A and B F n n . Prove that if ( I- AB ) is invertible then ( I- BA ) is invertible with inverse I + B ( I- AB )- 1 A . 7 Prove for A,B F n n that AB and BA have precisely the same characteristic values in F . 7 Suppose that A R 2 2 is symmetric. Prove that A is similar over R to a diagonal matrix. 7 Let N C 2 2 such that N 2 = 0. Prove that either N = 0 or N is similar over C to 0 0 1 0 . 7 If A C 2 2 show that A is similar over C to either a diagonal matrix or a matrix of the form s 1 s ....
View Full Document

This document was uploaded on 01/25/2012.

Page1 / 2

554-HW-7q - 7 Let T be the linear operator on R 4 which is...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online