Hi guys! This is my first post so hopefully you can help me out. I also am not sure how to edit the text to make it look better so if anyone wants to help me with that, Id be glad to clean up the post.

Here's the problem:

Let Mnxn be the collection of all nxn matrices. Defined is a linear transform P:

P: Mnxn --> Mnxn

A |--> P(A) = (1/2)*(A - A^T)

where A^T is the transpose of A.

What I already did was find KerP which is shown below:

KerP = {A: (1/2)*(A -A^T)=0} = {A = A^T}

That's all fine and dandy but I cant figure out how to find the basis for KerP without some numbers involved. If I had a matrix A with numbers, I could do it but I guess I cant figure out how to generalize it. My guess is that there wouldnt be a basis but I wouldnt know how to go about proving that either. Thanks for any help. I'll be online for at least the next 8 hours so I can reply quickly as well.