20.500.12556/RUL-188788 Thick compressions of thin algebras Let ${\mathcal A}$ 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. matrix algebra compression nonderogatory matrix operator system quantum clique diagonal algebra idempotent matrična algebra kompresija nederogatorna matrika operatorski sistem kvantna klika diagonalna algebra idempotent true false true Angleški jezik Slovenski jezik Članek v reviji 2026-09-28 10:55:35 2026-09-28 10:55:38 2026-09-29 04:06:20 0000-00-00 00:00:00 2027 0 0 Str. 273-298 Vol. 753 Jan. 2027 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2027-01-01 512:517.9 0024-3795 10.1016/j.laa.2026.09.017 292670723 1-s2.0-S0024379526003800-main.pdf 1-s2.0-S0024379526003800-main.pdf 1 3222545D855B45B10F24DF0CAFF069E4 3e5dae356199dac99544236e8338d7eeba3903f2a131e415c6d6a906b630489f 8dade415-bb1a-11f1-8bc5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=249120 https://www.sciencedirect.com/science/article/pii/S0024379526003800 1 497b895c-bb1a-11f1-8bc5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=249119 Fakulteta za matematiko in fiziko 0 0 0