Cramer, ZacharyMarcoux, Laurent W.Radjavi, Heydar2022-05-102022-05-102021-07-15https://doi.org/10.1016/j.laa.2021.03.005http://hdl.handle.net/10012/18252The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2021.03.005. © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 licenseAn algebra A of n × n complex matrices is said to be projection compressible if P AP is an algebra for all orthogonal projections P ∈ Mn(C). Analogously, A is said to be idempotent compressible if EAE is an algebra for all idempotents E in Mn(C). In this paper we construct several examples of unital algebras that admit these properties. In addition, a complete classification of the unital idempotent compressible subalgebras of M3(C) is obtained up to similarity and transposition. It is shown that in this setting, the two notions of compressibility agree: a unital subalgebra of M3(C) is projection compressible if and only if it is idempotent compressible. Our findings are extended to algebras of arbitrary size in [2]enAttribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)https://creativecommons.org/licenses/by-nc-nd/4.0/compressionprojection compressibilityidempotent compressibilityalgebraic cornersArticle