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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- May 22nd 2008, 08:56 PMUltros88Strictly 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

- May 22nd 2008, 09:51 PMmr fantastic
- May 23rd 2008, 11:35 AMUltros88Proof 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

- May 23rd 2008, 02:32 PMmr fantastic
Proof by induction will work (you have to know how to do matrix multiplication). See here: Matrix Algebra - Google Book Search