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This is a follow-up question to my question from Math Stackexchange (Thank you Dietrich Burde and Michael Burr for the help). Let $M\in \mathrm{SL}(4, \mathbb{Z})$ with all eigenvalues equal to $1$ (i....

Let $A$ and $B$ be finite dimensional algebras such that $A$ and $B$ are derived equivalent. Denote by $C_A$ (resp. $C_B$) the Cartan matrix of $A$ (resp. $B$). Then does the set of eigenvalues of $...

Given a $n \times n$ invertible matrix $A$, I am interested in the set $$ \mathcal{S}(A) = \{ D \textrm{ diagonal matrix } \mid \det(D - A) = 0 \}. $$ Thus, for all eigenvalues $\lambda_i$, we have $...

The wikipedia page for Cholesky decomposition says: For real matrices, the factorization has the form $A = LDL^T$ and is often referred to as LDLT decomposition. It is closely related to the ...

I would like to find the largest eigenvalue of an $n \times n$ binary matrix of density $p$, i.e., with $p n^{2}$ ones and $(1-p) n^{2}$ zeros. Any idea or reference is welcome.

Let $M=\begin{pmatrix} \begin{array}{cccccccc} 0 & 0 & 1 & 1 & 1 & 1 & 1 &1\\ 0 & 0 & 1 & 1 & 1 & 1 & 1 &1\\ 1 & 1 & 0 & 0 & ...