# Questions tagged [determinants]

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

498 questions
Filter by
Sorted by
Tagged with
546 views

• 41.7k
55 views

### Determinant of 2D non-positive second order partial differential operator

If I have an ordinary second order differential operator the Gelfand-Yaglom method is often useful to calculate its (regularized) determinant. The great advantage is that one doesn't have to calculate ...
184 views

• 5,510
36 views

### Fischer Information and Entropy, matrix case, determinant of covariance matrix going to zero

If $X \sim \mathcal{N}(\mu, \sigma^2)$, then \mathcal{I}\left(\mu, \sigma^2\right)=\left(\begin{array}{cc} \frac{1}{2\mathcal{H}...
122 views

### Is it express in terms of Schur Q-function?

Consider next integral \begin{eqnarray} Z \ = \ h^{- N N_f} \ \int\limits_{SU(N)} \ dU \ \prod_{n=1}^{N} \ \det \left ( 1 + h U \right )^{ N_f} \ \left ( 1 + h U^{\dagger} \right )^{ N_f} \ = \sum_{...
158 views

### Maximal minors of tensor product

Let $r \leq n$ be integers, and let $A$ be an $r \times n$ integer-valued matrix such that each $r\times r$ minor of $A$ is in $\{0, 1,-1\}$. Is it true that each $r^2 \times r^2$ minor of $A\otimes A$...
• 1,010
103 views

1 vote
144 views

### 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; ...
• 286
186 views

### 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 ...
• 275
198 views

• 51
413 views

### 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 ...
• 284
818 views

### 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. \...
• 1,503
223 views

### $\min(\det(\mathbf{A}))$ 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 ...
• 133