# Questions tagged [determinants]

Questions about the determinant of square matrices or linear endomorphisms. Also for closely related topics such as minors or regularized determinants.

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### Large sum of determinants of Hadamard products

We have $n$ by $n$ matrices $A$, $C$ and $S$ over a finite field $\mathbb{F}_q$. The $C$ is invertible of order $m$ as an element of $GL(\mathbb{F}_q,n)$. Is there an algorithm, polynomial in $n$, ...
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### Singularity of matrix pencil-like expression

I was working more on the topic on my previous question when I have to know whether the following statement is true to circumvent the "exception" caused by division by singular matrices; ...
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### A (bi)alternant formula for Wronskian

We know that there exists similarities between power functions and derivative of a function (in particular, Newton binomial formula and Leibniz rule for derivation of a product can be deduced from ...
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### One question on block-circulant matrices

Circulant matrices are very useful in digital image processing. I found the general formula for determinant of circulant matrix. But I think it is not suitable for block-circulant matrices. For ...
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### Determinant equal to Fibonacci sequence

I need to find the determinant of matrix defined by \begin{align*} & a_{i,1}=a_{1,j}=1,\quad \forall 1\leq i,j\leq n,\\ & a_{i,j}=a_{i-1,j}+a_{i,j-1}+i-j, \quad \forall 1< i,j\leq n. \...
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### $\min(\det(\mathbf{A}))$ for special matrix $\mathbf{A}$

(The construction of matrix $\mathbf{A}$ is not difficult to be understood. You can first jump to A Toy Example to take a glance. Any idea or suggestion would be appealing for me.) The Original ...
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### Possible values of the determinant for matrices with elements $\{1, 0, -1\}$

For matrices with elements $\{-1, 1\}$ it is known from here that the possible absolute values of determinants of $n \times n$, $n \leq 6$ matrices with entries $\{-1, 1\}$ are as follows: ...
1 vote
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### Determinant Inequality with unitary matrix

I come up with the following conjecture while doing my research, which is a determinant inequality. I have tried to run the MatLab simulation to verify its sanity. It seems that the inequality is true....
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### Lindström-Gessel-Viennot from properties of the $Alt^k$ functor?

Let $A$ be the directed adjacency matrix of an acyclic directed graph, with variables as its nonzero entries (one for each edge). The $(a,b)$ entry of the matrix $(I-A)^{-1}$ is the sum over all paths ...
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### Divisibility properties of minors of matrices

Let $A$ be an $m\times n$ matrix with integer entries. Let $d_i(A)$ be the greatest common divisor of all $i\times i$ minors of $A$, and define $d_0(A)=1$. Whenever $i\leq j$, one has that $d_i(A)$ ...
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