# Tagged Questions

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### Determinant of identity minus adjacency matrix

Let $M$ be the adjacency matrix of a directed graph $G$. Is there any known relation between $\det(\textrm{id}-M)$ and the cycles of $G$? It is easy to see that if $G$ is acyclic then this ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...
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 ...