0
votes
1answer
56 views

Determinant inequality for trace class operator

Let $A$ be a trace class operator on a Hilbert space. I wonder if there is an estimate of the form $$ |\log \det (I + A)| \le C\|A\|_1, $$ for some constant $C$, where the norm on the right is the ...
2
votes
1answer
61 views

determinant identity for invertible finite rank operators

I am currently reading a paper where the following identity, valid for an invertible finite - rank operator $T \colon \mathscr{H} \to \mathscr{H}$ on a separable Hilbert space, is given: $$ \log \det ...
3
votes
1answer
123 views

Skew symmetric matrix decomposes

I am supposed to show that for a skew-symmetric matrix $A$ with $det(A) \neq 0$, meaning that is has an even number of columns and rows, there is an invertible matrix $ R $ such that $ R^T A R = M$, ...
5
votes
1answer
219 views

A particular (functional) determinant calculation

One wants to calculate the quantity, $\det'(\frac{\partial}{\partial t} - i [\alpha, ])$ where the prime on the "det" means that one wants to do a product over only non-zero eigenvalues of the ...
3
votes
1answer
209 views

functional determinant

Let $w(x,y)$ be a real-valued symmetric function over the $[0,1]$x$[0,1]$ interval. We also know that if $n$ is an integer, and you pick $n$ values $x_i$ in the $[0,1]$ interval, then the matrix ...