If b is an indefinite symmetric bilinear form is it nondegenerate?
And conversely if b is nondegenerate is it positive/negative definite or indefinite?
How can i start to prove this? Note:Edited and changed the question
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
$b$ is indefinite iff its matrix representation $B$ has both positive and negative eigenvalues; $b$ is nondegenerate iff $B$ has no zero eigenvalues. So,