Question

How to solve it? find a basis of C^2 such that the matrix with respect to that basis is triangular
\[\left[\begin{matrix}1&1\\1&0\end{matrix}\right]\]
Please, help

Answer 1

@tkhunny

Answer 2

eigenvalues: \(\lambda_1 = \dfrac{1+\sqrt{5}}{2}\) and \(\lambda_2 = \dfrac{1-\sqrt{5}}{2}\)

Answer 3

but they are so ugly eigenvectors so that I can't step up finding out the triangular matrix A with respect to that basis

Answer 4

Haha, well I'm not entirely sure what you're looking for here. Are you just trying to diagonalize this matrix?

Answer 5

if it 's just diagonalize, I am get A for the course. hahahaha...
let me attach one which I can get the result for you to know what I am doing. :)

Answer 6

Sure, I am pretty good with change of basis and transformation kind of stuff, I think we can probably figure this out together.

Answer 7

thanks for being here :)

Answer 8

here is another one

Answer 9

I am sort of messed up I guess after finding the first eigenvector for 56.1 I am sort of lost with what's going on I'm afraid.

Answer 10

this is lecture from the book and the exercise is on the last page

Answer 11

Thanks for support. need sleep now.