A Simultaneous Cholesky Decomposition of Two Positive Definite Matrices

• 발행기관: 한국자료분석학회
• 저자명: 박종태(Jong Tae Park)
• 간행물 정보: 『Journal of The Korean Data Analysis Society (JKDAS)』Vol.7 No.1, 81~87쪽, 전체 7쪽
• 주제분류: 자연과학 > 통계학
• 파일형태: PDF
• 발행일자: 2005.02.28

영문 초록

In this paper we consider the simultaneous diagonalization of two positive definite matrices. A necessary and sufficient condition is found under which two positive definite covariance matrices are simultaneously diagonalized in view of a Cholesky decomposition. This result can be applied to estimating the eigenvalues and eigenvectors of for two positive definite covariance matrices ,. under multivariate normality. The result is extended to more than two matrices. The result is also applied to computing the conditional expectations contained in some decompositions of the Mahalanobis distance that help us to explain some reasons for the outlyingness of multivariate observations in multivariate analysis. Since the Cholesky decomposition of covariance matrix is useful in expressing the conditional expectation of one variable when the remaining variables are fixed under multivariate normality. An example is given for an illustration.

목차

1. Introduction

2. The main results

3. An Example

References

키워드

Cholesky decomposition Cholesky root Diagonalization Positive definite matrix