Thick compressions of thin algebrasOmladič, Matjaž (Avtor) Radjavi, Heydar (Avtor) Šivic, Klemen (Avtor) Zalar, Aljaž (Avtor) matrix algebracompressionnonderogatory matrixoperator systemquantum cliquediagonal algebraidempotentLet ${\mathcal A}$ be the algebra generated by a nonderogatory matrix in $M_{n^2}({\mathbb F})$, where ${\mathbb F} = {\mathbb C}$ or ${\mathbb R}$. We prove that there exist matrices $V \in M_{n^2,n}({\mathbb F})$ and $W \in M_{n,n^2}({\mathbb F})$ such that $WV = I_n$ and $W{\mathcal A}V = M_n({\mathbb F})$. Over ${\mathbb C}$, this is equivalent to the existence of a rank $n$ orthogonal projection $P$ for which $P{\mathcal A}P|_{{Rm Im} P} = M_n({\mathbb C}$. As a consequence, the diagonal algebra in $M_{n^2}({\mathbb F})$ has a quantum $n$-clique. The corresponding optimal result for the complex diagonal algebra was recently obtained independently by Weaver. Over ${\mathbb R}$, ordinary orthogonal compressions are generally too restrictive, and the corresponding geometric result is formulated using general rank-$n$ idempotents, possibly oblique. We also give an elementary two-sided construction for the diagonal algebra over both fields and determine the dimensions of the other three block spaces associated with a maximal orthogonal compression of a commutative self-adjoint algebra.20272026-09-28 10:55:35Članek v reviji188788UDK: 512:517.9ISSN pri članku: 0024-3795DOI: 10.1016/j.laa.2026.09.017COBISS_ID: 292670723sl