[SOLVED]The Meaning of Degenerate in the Context of Linear Algebra

Sudharaka

Well-known member
MHB Math Helper
Hi everyone,

Here's a question I encountered.

Show that $$f(x)\rightarrow f'(x)$$ is degenerate on $$R[x]_{n}$$ and is non-degenerate on $$<\sin t,\,\cos t>$$
Don't give me the full answer but explain what is meant by degeneracy in this context.

Thank you.

Deveno

Well-known member
MHB Math Scholar
It means the derivative map has a non-trivial null space.

Sudharaka

Well-known member
MHB Math Helper
It means the derivative map has a non-trivial null space.
Thank you very much. Now I understand it perfectly. I am doing an Advanced Linear Algebra course and I am not getting everything perfectly. I think I have to put a lot of effort into it.