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Question about linear algebra (upper triangular matrices)

http://www2.imperial.ac.uk/~mwl/m2p2/M2P210SH9.PDF

How would I do number 1? I know that such a matrix exists because it was proven. But the proof was by induction and I didn't fully understand it. So how do I find this matrix?

Reply 1

nuodai

I'm not sure how you've been taught this, but there are many ways you can do it. For example you can put the matrix in Jordan normal form, or find the eigenvectors and use them as a basis, etc...

Reply 2

gangsta316

Original post by nuodai

I'm not sure how you've been taught this, but there are many ways you can do it. For example you can put the matrix in Jordan normal form, or find the eigenvectors and use them as a basis, etc...

Wouldn't the eigenvectors method be for diagonalization? If we get the Jordan canonical form then we would have an upper triangular matrix but how do we find the invertible matrix P?