Do n-by-n traceless matrices form a vector space over the field C of complex numbers? Why or why not? If yes, show a basis and give the dimension of the vector space!
Over the field R of real numbers, I know that they form a vector space:
0 matrix is in the vector space
-A matrix is in
But I don't know what is a basis over real numbers.
And I don't even know if they form a vector space over the field C of complex numbers. I suppose they do, but I am not sure, I can't prove it.
Your help would be appreciated.