Questions tagged [determinant]
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questions
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Numerically stable way to implement Cramer's rule analog
Problem statement
Let $A$ be an $n\times n$ matrix and $b$ an $n$-dimensional vector. For $j\in \{1, \dots, n \}$, let $A_j$ be the matrix where we take $A$ and replace the $j^{\rm th}$ column with $b$...
- 31
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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 $\det(X)=\pm\det(S)$...
- 153
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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?
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