Determine whether the function is a linear transformation (Attempt inside)

[sam0617]

T: M_nn => R, where T(A) = tr(A)

Attempt:

1) T(kA) = tr(kA) = k tr(A) = k T(A)



2) T(A+B) = tr (A + B) = tr(A) + tr(B) = T(A) + T(B)

so it's linear transformation. Am I correct?

 

[Deveno]

technically, yes, but if that was homework, and i were grading it, i don't think i'd give it full marks.

you should show a little more work, you haven't used the definition of trace anywhere...