✦ LIBER ✦

A determinantal proof of the Craig-Sakamoto theorem

✍ Scribed by Ingram Olkin

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 183 KB
Volume: 264
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(96)00484-3

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✦ Synopsis

The Craig-Sakamoto theorem states that if A and B are symmetric matrices, then (a) II -ctA -flBI = II -aAI II -/3BI for all a, /3 if and only if (b) AB = O. There are a number of proofs of this resttlt, the most common based on expansions of the logarithm of (a). The present proof is elementary in that it depends only on determinantal conditions.

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