# [1]朱道元,赵桂芹.Bartlett 分解定理的简便证明[J].东南大学学报(自然科学版),2001,31(5):125-127.[doi:10.3969/j.issn.1001-0505.2001.05.027] 　Zhu Daoyuan,Zhao Guiqin.A Concise Proof of the Bartlett Decomposition Theorem[J].Journal of Southeast University (Natural Science Edition),2001,31(5):125-127.[doi:10.3969/j.issn.1001-0505.2001.05.027] 点击复制 Bartlett 分解定理的简便证明() 分享到： var jiathis_config = { data_track_clickback: true };

31

2001年第5期

125-127

2001-09-20

## 文章信息/Info

Title:
A Concise Proof of the Bartlett Decomposition Theorem

Author(s):
Department of Applied Mathematics, Southeast University, Nanjing 210096, China)

Keywords:

O212.1
DOI:
10.3969/j.issn.1001-0505.2001.05.027

Abstract:
For a random matrix that represents the Whishart distribution, there exists the well-known Bartlett decomposition theorem. The result is perfect, but the proof is tedious. This article uses the characteristic function to prove the following result: the inner product of two independent (n-i+1)-dimensional random vectors subject to standard normal distribution has the same distribution of the product of two independent random variables in which one is subject to χn-i+1 distribution and the other to N(0,1) distribution. Thus the theorem can be proved briefly and directly. Though the conclusion is reduced to W=dT′T, it does not affect the application of Bartlett decomposition theorem in most cases.

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