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Some inequalities for the rational power of a nonnegative definite matrix

โœ Scribed by Yik-Hoi Au-Yeung

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
125 KB
Volume
7
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

In this note the author gives a simple proof of the following fact: Let r and s be two positive rational numbers such that r ~ s and let A and B be two n ร— n nonnegative definite Hermitian matrices such that Ar~ B r. Then AS~ B s.

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โœ Zizhen Chen; Zhongdan Huan ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 162 KB

In this paper we prove that the mth root of a nonnegative definite matrix-valued function with continuous entries is continuous. In particular, if all the entries are , which generalizes the result on the square ลฝ .