1
vote
1answer
46 views

Trace of the exterior power as a determinant

Let $A$ be a matrix. According to Wikipedia, $$tr(\wedge^k A) = \frac{1}{k!} \det \begin{pmatrix} tr (A) & k-1 & 0 & \cdots \\ tr (A^2) & tr (A) & k-2 & \cdots \\ \cdots & ...
1
vote
0answers
159 views

Determinant of symmetric block matrix

I have a block matrix of the form: $B = \left[\begin{array}{cccc} A_1 & C & \dots & C\\ \vdots & A_2 & \dots & C\\ C & \vdots & \ddots & \vdots\\ C & C & C ...
2
votes
0answers
45 views

Reference request on pseudo-determinants

I am looking for a reference on pseudo-determinants$^{(1)}$. I am mostly interested on general and/or basic equalities and properties such as those obtained for determinants. Any pointers would be ...
1
vote
1answer
103 views

looking for paper by Chapman on determinant of sum of matrices

Math people: I am trying to find a paper by Chapman referenced after Remark 2.3 in the paper "On the elementary symmetric functions of a sum of matrices" by R. S. Costas-Santos posted on the arXiv ...
2
votes
3answers
142 views

On integral of a function over a simplex

Help w/the following general calculation and references would be appreciated. Let $ABC$ be a triangle in the plane. Then for any linear function of two variables $u$. $$ \int_{\triangle}|\nabla ...
10
votes
2answers
510 views

Do determinants of binary matrices form a set of consecutive numbers?

While pondering a solution for the problem of generating random 0-1 matrices with small absolute determinants, I once again realise how little I know about 0-1 matrices. My initial idea was to pick a ...
3
votes
2answers
127 views

Textbook determinant convention

My text book is called "Linear Algebra and its applications" by David C. Lay. I am just wondering why the textbook uses the absolute value symbol when it wants us to compute determinants. For ...
0
votes
1answer
204 views

Inequalities involving determinants and minors of positive definite matrices

Lately I've been dealing with positive definite matrices in my research (in the context of them being covariance matrices), and, am wondering if anyone knows of a comprehensive list of inequalities ...
1
vote
1answer
2k views

determinant of a sum

I need a formula for the determinant of the sum of two matrices: $\det(\mathbb{I}+M)$. On the internet I found it for the first order but i need it at second or even third order. Where can I find the ...
5
votes
0answers
118 views

Determinant expression for the power sum

Let $S_{n,r} := \sum_{k=1}^{n} k^r$ be the power sum. On the homepage by W. Hecht (link) I have found the following determinant expression: $$S_{n,r} = (-1)^{r-1} \frac{n(n+1)}{(r+1)!} \det ...