Questions tagged [determinant]
The determinant tag has no summary.
6 questions
6 votes
1 answer
232 views
Feasibility of computing large determinants
I have a dense $10^6\times10^6$ matrix having entries in $[-2^m+1,2^m-1]\cap\mathbb Z$. What resources do I require in $2025$ state of the art for computing the determinant in a reasonable time of say ...
- 231
5 votes
0 answers
149 views
Determinant of matrix square root
I have a complex-symmetric matrix $A$ of size $n\times n$ with positive real part $\Re(A)>0$, and I need to calculate $$\det\left(\sqrt{A}\right)$$ in the context of calculating a Gaussian integral....
- 203
10 votes
5 answers
1k 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 ...
- 109
2 votes
1 answer
227 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 $b$...
- 31
2 votes
2 answers
374 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 $\det(X)=\pm\det(S)$...
- 203
1 vote
1 answer
505 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?
- 183