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Questions tagged [determinant]

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10 votes
5 answers
911 views

How to efficiently compute the determinant of a matrix with unknown diagonal entries?

I would like to ask Python to compute the determinant of a large symmetric matrix where all off diagonal entries are known. The diagonal entries could vary. Since I need to compute the determinant ...
dangqingdouna's user avatar
2 votes
1 answer
173 views

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
294 views

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
315 views

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