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Math Help - Strictly Upper Triangular Matrix Proof Help Needed

  1. #1
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    Cool Strictly Upper Triangular Matrix Proof Help Needed

    Hey, I'm trying to prove that for a strictly upper triangular matrix A, A^n = 0. I'm pretty much stuck at writing down the definition for matrix multiplication for A*A. Any help/hints would be much appreciated. Thanks, Ultros
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    Quote Originally Posted by Ultros88 View Post
    Hey, I'm trying to prove that for a strictly upper triangular matrix A, A^n = 0. I'm pretty much stuck at writing down the definition for matrix multiplication for A*A. Any help/hints would be much appreciated. Thanks, Ultros
    A is nilpotent. Show either that its eigenvalues are all zero or that its determinant is zero.
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    Proof Excercise Comes Before Nilpotents/Determinants

    Is there a way to prove that A^n = 0 without using the fact that its determinant or eigenvalues are all zero? This exercise comes before those topics in the book that I am using. Thanks
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    Quote Originally Posted by Ultros88 View Post
    Is there a way to prove that A^n = 0 without using the fact that its determinant or eigenvalues are all zero? This exercise comes before those topics in the book that I am using. Thanks
    Proof by induction will work (you have to know how to do matrix multiplication). See here: Matrix Algebra - Google Book Search
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