Recent content by Sanglee

So clear, easy to understand. Thanks!

Homework Statement Let V be the spcae of all 3x3 matrices with real entries. Is W, the set of all 3x3 lower triangular matrices, a subspace of V? Why or why not? Homework Equations The Attempt at a Solution I just think that all 3x3 lower triangular matrices are included in...

Homework Statement Suppose V is a vector space. Is the set of all 2x2 invertible matrices closed under addition? If so, please prove it. If not, please provide a counter-example. Homework Equations The Attempt at a Solution well i know that what does it mean to be closed...

Oh, i understand it now :) Thanks!

Oh~~~~~~~~I got it! it's really simple question, but I thought it was complicated. hehe So, A and inverse of A are similar, so their eigenvalues are same. if one of A's eigenvalues is n, a eigenvalues of its inverse will be 1/n. But the two matrices are similar, so n=1/n Then, n^2=1, so...

Homework Statement If A is similar to A^(-1) (=inverse of A), must all the eigenvalues equal 1 or -1? Homework Equations The Attempt at a Solution I don't know why the textbook gives me the specific value 1 or -1. If A is similar to its inverse, are the eigenvalues really 1 or...