Question
True or false: All the eigenvalues of an $n \times n$ permutation matrix are real.
Step 1
A permutation matrix is a square binary matrix (elements are 0 or 1) that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each permutation matrix corresponds to a specific permutation of the set {1, 2, ..., n}. Show more…
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True or false: If the $n$ columns of $S$ (eigenvectors of $A$ ) are independent, then (a) $A$ is invertible. (b) $A$ is diagonalizable. (c) $S$ is invertible. (d) $S$ is diagonalizable.
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