Recent content by jsgoodfella

How do you show that a set of linear transformations from one vector space to another spans L(V,W)? This isn't a homework question, or even a question that's in the text I'm reading (Friedberg).

Thanks for your help! Just to make sure, the dimension is p-squared, right?

Thanks for staying with me! I'm thinking of the general basis for p^2 - If p is two, then [{0,1};{0,0}] could be a matrix in the basis which doesn't represent a linear transformation. Do we just assume they are all linear? On another note, is there a linear transformation that maps...

Well, we know that each matrix is pxp, because Z is p-dimensional. The dimension of this space of matrices is p-squared (for instance there are 4 basis matrices for the 2x2 case). But how can we know that each matrix in the p^2 dimensional basis is a linear matrix?

If we consider the set R of all linear transformations from an p-dimensional vector space Z to Z (T:Z -> Z), what do we know about the dimension of the set R? In other words, what do we know about any basis for R? What are its properties?

If we take an nxn diagonal matrix, and multiply it by an nxn matrix C such that AC=CA, will C be diagonal? I know, for instance, if C is a matrix with ones in every entry, AC=CA holds. But is there a more general way to format such a counterexample, or have I already provided a sufficient...