# 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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QUESTION. Is my following conjecture true? If true, how to prove it? Conjecture. Let $p$ be a prime with $p\equiv5\pmod 6$, and define the matrices $A_p$ and $B_p$ by $$A_p:=\left[\frac1{i^2-ij+j^2}\... 0answers 134 views ### Non-trivial ways for generating matrices A for which A + A^T is positive-definite? Disclaimer: This might be an SE question, but I'm not quite sure... Thanks in advance! Setup So, it is known (see Proposition 5.2) that if A + A^T is positive-definite then A must be a P-... 2answers 515 views ### Classification of algebras of finite global dimension via determinants of certain 0-1-matrices I restrict to the elementary problem that is equivalent to give a classification when Morita-Nakayama algebras have finite global dimension (see the end of this post for some background). A Morita-... 2answers 227 views ### Equal-valued determinants in search of a proof: Part III Encouraged by David's proof for my earlier MO question, let's consider a similar problem. I can prove the below equality by computing each of the two sides, directly. That means, there is an ... 1answer 457 views ### Catalan determinants in search of a proof: Part II This problem involves the Catalan numbers C_n=\frac1{n+1}\binom{2n}n. I can prove the below equality by computing each of the two sides, directly. That means, there is an algebraic proof. ... 1answer 275 views ### Deligne Pairing v.s. Weil Pairing on a Family of curves We have the Deligne Pairing on a family of curve \pi:X\to S by using$$\langle L,M\rangle_{\mathrm{Pic}^0(X/S)}=\det R\pi_*(L\otimes M) \otimes (\det R\pi_*L)^{-1}\otimes (\det R\pi_*M)^{-1} \otimes ...
Consider the determinantal function $$F(a,b,c):=\det\left[\binom{i+j+a+b}{i+a}\right]_{i,j=0}^{c-1}.$$ I would like to ask: QUESTION. Can you provide an argument, combinatorial or otherwise, to ...
### Coordinate free expression for the determinant of a $2 \times 2$ matrix
Let $E\rightarrow X$ be a rank two vector bundle on a variety $X$. How can one write an abstract map $Sym^2(E)\rightarrow (\wedge^2 E)^{\otimes 2}$ that in local coordinates, when we fix a frame of $E$...