Marcoux, Laurent W.Radjavi, HeydarZhang, Yuanhang2022-05-102022-05-102020-12-15https://doi.org/10.1016/j.laa.2020.07.036http://hdl.handle.net/10012/18254The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2020.07.036. © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 licenseLet n ∈ N, and consider Cn equipped with the standard inner product. Let A ⊆ L(Cn) be a unital algebra and P ∈ L(Cn) be an orthogonal projection. The space L := P ⊥A|ran P is said to be an off-diagonal corner of A, and L is said to be essential if ∩{ker L : L ∈ L} = {0} and ∩{ker L ∗ : L ∈ L} = {0}, where L ∗ denotes the adjoint of L. Our goal in this paper is to determine effective upper bounds on dim A in terms of dim L, where L is an essential off-diagonal corner of A. A detailed structure analysis of A based upon the dimension of L, while seemingly elusive in general, is nevertheless provided in the cases where dim L ∈ {1, 2}.enAttribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)off-diagonal cornerscompressions of matricesArticle