Questions tagged [determinant]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2 votes
1 answer

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 $b$...
Joe's user avatar
  • 31
2 votes
2 answers

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 $\det(X)=\pm\det(S)$...
cheetah's user avatar
  • 153
1 vote
1 answer

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?
5d41402abc4's user avatar