Maximal normal sets of \(n\)-planes in \({\mathbb{R}{}}^{2n}\)
type: Item
instance of: scholarly article
title: Maximal normal sets of \(n\)-planes in \({\mathbb{R}{}}^{2n}\)
zbMATH Open document ID: 0784.15016
DOI: 10.1016/0024-3795(93)90033-K
published in: Linear Algebra and its Applications
publication date: 1993-05-16T00:00:00Z
review text: The paper investigates the relation between the notions of maximal normal sets and maximal isoclinic sets of \(n\)-planes in \(R^{2n}\). Two \(n\)- planes \(A\) and \(B\) in \(R^{2n}\) are normally related if the intersection of \(A\) and \(B\) and also of \(A\) and the orthogonal complement of \(B\) both are 0. A normal set is a set of \(n\)-planes such that every two distinct \(n\)-planes are either orthogonal or normally related. Two \(n\)-planes are isoclinic if the angle between an arbitrary vector in one plane and its orthogonal projection on the other plane remains constant. An isoclinic set is a set of mutually isoclinic \(n\)-planes. It is shown that every maximal normal set that is parametrized by a subspace of nonsingular matrices is a maximal isoclinic set. Conversely it is proved by methods from homotopy theory: Every maximal isoclinic set is a maximal normal set.
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 167843
zbMATH Keywords: set of \(n\)-planes
zbMATH Keywords: maximal normal sets
zbMATH Keywords: maximal isoclinic sets
author: Paul Yiu
reviewed by: Tage Bai Andersen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 167843