Permutation Matrices: Proving P Inverse = P Transpose

Thread starter EvLer
Start date Sep 12, 2006
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Matrices Permutation

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Permutation matrices are square matrices that represent row interchanges of the identity matrix. The key property discussed is that the inverse of a permutation matrix P is equal to its transpose, denoted as P^T. This relationship holds because the rows of P form an orthonormal basis in R^n, which leads to the conclusion that PP^T equals the identity matrix. Understanding this property is essential for various applications in linear algebra and combinatorics. The discussion emphasizes the importance of recognizing the structure of permutation matrices in proving this relationship.

Sep 12, 2006

EvLer

I can't proove why P inverse = P transpose always!
P is the permuation matrix, i.e. a matrix is identity but the rows can be interchanged.
Thanks in advance.

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Sep 13, 2006

matt grime

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I can offer no other advice than that you should just write down PP^t (the rows of P are an ******* basis of R^n - fill in the *******).

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