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Math Help - Linear Algebra.Similar to a triangle matrix.pls help!

  1. #1
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    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.

    Thanks in Advance
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  2. #2
    Super Member Showcase_22's Avatar
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    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?
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  3. #3
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    Quote Originally Posted by Showcase_22 View Post
    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.
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  4. #4
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    Quote Originally Posted by ypatia View Post
    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.

    Thanks in Advance
    Perhaps studying some on-line lessons from here will help: similar matrices - Google Search
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