A simple proof of the Craig–Sakamoto theorem
✍ Scribed by Chi-Kwong Li
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 51 KB
- Volume
- 321
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
We give a simple proof of the Craig±Sakamoto theorem, which asserts that two real symmetric matrices A and B satisfy detI
📜 SIMILAR VOLUMES
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
This article gives a simple proof of a result of Moser, which says that, for any rational number r between 2 and 3, there exists a planar graph G whose circular chromatic number is equal to r.
## Abstract A proof of Menger's theorem is presented.