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Close to the Craig–Sakamoto’s theorem

✍ Scribed by Hervé Carrieu


Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
86 KB
Volume
432
Category
Article
ISSN
0024-3795

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We give a simple proof of the Craig±Sakamoto theorem, which asserts that two real symmetric matrices A and B satisfy detI

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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 t