What is It's not diagonalizable.
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Originally Posted by Spec What is It's not diagonalizable.
Originally Posted by Spec What is It's not diagonalizable. one way is to use induction to show that a better way, which can be used for more complicated matrices, is to write where is the identity matrix and then and commute. then by the binomial theorem:
Originally Posted by NonCommAlg I don't get that part. I know what the binomial theorem says, but I've never seen it used on matrices. EDIT: Nevermind, I didn't see the B^2 part.
Originally Posted by Spec I don't get that part. I know what the binomial theorem says, but I've never seen it used on matrices. EDIT: Nevermind, I didn't see the B^2 part. this is a good method of finding powers of matrices. as another example we want to find where so we let then and again commute and so we can use binomial theorem, which gives us:
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