I have no idea what you mean by "LA". How is it defined?How is LA a linear function? What kind of operation is action on A? I thought L denotes a linear transformation. So if we have a matrix A, how is the LA a transformation? Is it just a definition (notation wise) or is there more to it?
THanks, that's exactly what I thought. However, in the text I am reading, it says L_A is linear immediately from theorem 2.12:If A is an m*n matrix, then the mapping [tex]L_A[/tex] is from F^m to F^n and is defined by [tex] L_A(x) = Ax [/tex]. If [tex] x_1 [/tex] and [tex] x_2 ][/tex] are vectors in F^n, then [tex] L_A (x_1 + x_2) = A(x_1 + x_2) = Ax_1 + Ax_2 = L_A(x_1) + L_A(x_2) [/tex]. Also, for any vector x in F^n and any scalar c, we have [tex] L_A(cx) = A(cx) = cAx = cL_A(x) [/tex]. Thus [tex] L_A [/tex] is a linear transformation.