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

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
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
Feb 15, 2012
1,967
It means the derivative map has a non-trivial null space.
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
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. :)