A generalization of the rotation matrix and related results
type: Item
instance of: scholarly article
title: A generalization of the rotation matrix and related results
zbMATH Open document ID: 0623.15015
DOI: 10.1016/0024-3795(87)90262-X
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: Let z be an independent complex variable. The author shows that applying the exponential map to z times the \(n\times n\) circulant matrix (skew circulant matrix), whose first row is 0,1,...,0, gives the circulant (skew circulant) matrix whose first row consists of the hyperbolic (trigonometric) functions of order n. This result provides a new generalization of the \(2\times 2\) rotation matrix, as well as a unified treatment of some properties of that generalization and of the matrices considered by \textit{A. Ungar} [Am. Math. Mon. 89, 688-691 (1982; Zbl 0529.33001)]. Infinitesimal generators and invariants of the corresponding Lie groups of transformations are obtained.
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 22E99
zbMATH DE Number: 4010697
zbMATH Keywords: exponential map
zbMATH Keywords: trigonometric functions of order n
zbMATH Keywords: hyperbolic functions of order n
zbMATH Keywords: skew circulant matrix
zbMATH Keywords: rotation matrix
zbMATH Keywords: Infinitesimal generators
zbMATH Keywords: Lie groups of transformations
author: R. Kit Kittappa
reviewed by: Mark Kleiner
MaRDI profile type: Publication
cites work: Q3208805
cites work: Q3860029
cites work: Q5824493
cites work: Q5345657
cites work: Generalized Hyperbolic Functions
description: scientific article; zbMATH DE number 4010697