1
vote
0answers
69 views

Does this permanent have a closed form?

What is the closed form of this permanent? (similar to the Cauchy determinant) \begin{aligned} f(z_1,z_2,\cdots,z_N,w_1,w_2,\cdots,w_N)=\left[ \small{\begin{matrix} \frac{1}{(z_1-w_1)^2} && ...
7
votes
1answer
209 views

Block Matrix determinant

Consider the $k \times k$ block matrix: $ C = \left(\begin{array}{ccccc} A & B & B & \cdots & B \\ B & A & B &\cdots & B \\ \vdots & \vdots & \ddots & ...
9
votes
1answer
411 views

M-matrix plus S-matrix is P-matrix?

I am trying to prove that a mapping has a unique fixed-point by showing that its Jacobian is a P-matrix. In this particular case the Jacobian can be decomposed as the sum of two matrices and I would ...
0
votes
1answer
213 views

Bounding a determinant ratio

Let $A=[A_{0}\ E;E^{T} \ B]$ be a real positive definite matrix and let $B$ be a principal submatrix. I am interested in tightly bounding $\frac{|B|}{|A|}$ from below in some "explicit" way that will ...