The determinants tag has no wiki summary.

**0**

votes

**1**answer

505 views

### Hankel determinants of symmetric functions

The starting point is that it is known that the Hankel determinants for the Catalan sequence give the number of nested sequences of Dyck paths. I would like to promote this to symmetric functions.
...

**21**

votes

**3**answers

2k views

### Splitting the determinant polynomial into linear factors - a Dedekind problem

Here's the question in a nutshell. For some $n\in\mathbb N$, we consider the polynomial
$\det\left(\left(X_{i,j}\right) _ {1\leq i\leq n,\ 1\leq j\leq n}\right)\in\mathbb Z\left[X_{i,j}\mid 1\leq ...

**9**

votes

**2**answers

1k views

### What are picard categories, where can I learn more about them, and why should I care to?

I have the category-theoretic background of the occasional stroll through Mac Lane's text, so excuse my ignorance in this regard. I was trying to learn all that I could on the subject of tensor ...

**6**

votes

**3**answers

1k views

### Sarrus determinant rule: references, extensions

SEEKING REFERENCES FOR SARRUS' RULE AND EXTENSIONS
An undergraduate came to me with an identity for 4x4 determinants that is actually correct:
$\det(A)=h(A)+h(RA)+h(R^{2}A)$
where R cyclically ...

**18**

votes

**2**answers

1k views

### Lifting matrices mod 2 to integers.

The following question was motivated by my research.
Consider a $n\times n$ matrix whose elements are $0$'s or $1$'s such that the determinant is odd. The question is: is it possible to assign signs ...

**2**

votes

**2**answers

1k views

### Statement of Lagrange's theorem on determinants(elementary question).

Apologies for this elementary question; but I was unable to find a reference otherwise.
Let $A, B, C$ be square matrices of the same dimension. Then,
$$\begin{vmatrix} A & C \\\ 0 & B ...

**4**

votes

**2**answers

541 views

### What's the correct notion of determinant of a bilinear pairing?

By a pairing on a vector space $V$, I mean a linear map $A : V \otimes V \to R$. If $V$ is $n$-dimensional ($n < \infty$), then I can define the determinant of $A$ by considering the canonical ...