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 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...