International Statistical Review

The Trigonometry of Matrix Statistics

Karl Gustafson

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Abstract

A matrix trigonometry developed chiefly by this author during the past 40 years has interesting applications to certain situations in statistics. The key conceptual entity in this matrix trigonometry is the matrix (maximal) turning angle. Associated entities (originally so-named by this author) are the matrix antieigenvalues and corresponding antieigenvectors upon which the matrix obtains its critical turning angles. Because this trigonometry is the natural one for linear operators and matrices, it also is the natural one for matrix statistics.

Article information

Source
Internat. Statist. Rev., Volume 74, Number 2 (2006), 187-202.

Dates
First available in Project Euclid: 24 July 2006

Permanent link to this document
https://projecteuclid.org/euclid.isr/1153748792

Mathematical Reviews number (MathSciNet)
MR2240293

Keywords
Operator trigonometry Antieigenvalue Antieigenvector Parameter estimation Watson statistical efficiency Canonical correlation Rayleigh-Ritz theory

Citation

Gustafson, Karl. The Trigonometry of Matrix Statistics. Internat. Statist. Rev. 74 (2006), no. 2, 187--202. https://projecteuclid.org/euclid.isr/1153748792


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