In my linear algebra course I have a problem which goes as follows:
Suppose A is an nxn matrix over field (R) And J(A) is the jordan form of A.
Given α belongs to field R, what is the jordan form of αA?
I have worked out, through trial and error, that the jordan form of αA is simply J(A) with the elements (the different eigenvalues) along the diagonal multiplied by α.
I couldnt think of a formal proof for this problem, I think it might be some simple characteristic I may have overlooked.
Any help is appreciated Thanks!