
Originally Posted by
aman_cc
Hi - Need help in understanding the following
Let
X be a n-dim vector space
Y be a m-dim vector space
A be a mxn matrix
Thus, AX defined a linear transformation,T from X into Y i.e. T: X -> Y
Image of X under T, T(X) is a subspace of Y
I need help in understanding and thus formally proving two concepts:
1. Rank of A (which say is defined as dim of row space or dim of col space) = dim of T(X)
2. Why is dim(row space of A) = dim(col space of A)
Any pointers would be welcome. Thanks