Questions tagged [determinant]

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Calculate determinant of unitary matrices based on SVD implementation

I have a real square matrix $X$ which I need to perform a Singular Value Decomposition on. Now, performing the operation $$ X = USV^T $$ as $U$ and $V$ are orthogonal, we know that $\det(X)=\pm\det(S)$...
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How to compute the determinant of a permutation matrix

Let $\mathbf{P}$ be a permutation matrix (i.e. a matrix that is all zeros except for a single one in each row). Is there an efficient algorithm for computing the determinant of such a matrix?