# Linear Algebra.Similar to a triangle matrix.pls help!

• Mar 22nd 2009, 12:47 AM
ypatia
Linear Algebra.Similar to a triangle matrix.pls help!
We have the following matrix :

$A=\begin{pmatrix} 2 &0&0 \\ 0&0&1 \\ 0&-1&0 \end{pmatrix}$

How can I found a triangle matrix similar to the initial matrix.

I was pleased if someone show me the step by step solution because I have 2 more matrices to do exactly the same procedure.

• Mar 22nd 2009, 07:27 AM
Showcase_22
Here's my idea: Find the eigenvalues of the matrix A and put them into a diagonal matrix.

Since a diagonal matrix is both upper and lower triangular, it's triangular.

Is there anything wrong with this idea?
• Mar 22nd 2009, 10:55 AM
ypatia
Quote:

Originally Posted by Showcase_22
Here's my idea: Find the eigenvalues of the matrix A and put them into a diagonal matrix.

Since a diagonal matrix is both upper and lower triangular, it's triangular.

Is there anything wrong with this idea?

This is right (diagonal matrix is both upper and lower triangular) but I think that the exercise asks to find exactly a triangular matrix which mean something less than you refer(diagonal). Anyway thanks alot for replying my post.
• Mar 29th 2009, 01:27 AM
mr fantastic
Quote:

Originally Posted by ypatia
We have the following matrix :

$A=\begin{pmatrix} 2 &0&0 \\ 0&0&1 \\ 0&-1&0 \end{pmatrix}$

How can I found a triangle matrix similar to the initial matrix.

I was pleased if someone show me the step by step solution because I have 2 more matrices to do exactly the same procedure.