Steven G
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- Dec 30, 2014
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Theorem: If Matrix A is skew symmetric then A^K is skew symmetric for any positive integer K.
The above is a theorem in my Linear Algebra book.
However I have reasons to think it is wrong. Can someone please point out the error in my counterexample.
1st I will tell you what I know. For A to be skew symmetric we must have A^T= -A. Also (AB)^T = B^T*A^T
Suppose A is skew symmetric. Then (A2)T=(AA)T= ATAT (-A)(-A) = A2 and not -A2
The above is a theorem in my Linear Algebra book.
However I have reasons to think it is wrong. Can someone please point out the error in my counterexample.
1st I will tell you what I know. For A to be skew symmetric we must have A^T= -A. Also (AB)^T = B^T*A^T
Suppose A is skew symmetric. Then (A2)T=(AA)T= ATAT (-A)(-A) = A2 and not -A2