The Meaning of Degenerate in the Context of Linear Algebra

[Sudharaka]

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]

It means the derivative map has a non-trivial null space.

 

[Sudharaka]

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. :)