## International Statistical Review

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

### The Trigonometry of Matrix Statistics

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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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