Does this mean a matrix always represents a linear map?
motoole2
Yes! A matrix-vector multiplication is a linear map because it shares the definition above, i.e., A*u = \sum u_i a_i where a_i is the i-th column of matrix A (and satisfies all the properties associated with linear maps).
Does this mean a matrix always represents a linear map?
Yes! A matrix-vector multiplication is a linear map because it shares the definition above, i.e.,
A*u = \sum u_i a_iwherea_iis the i-th column of matrixA(and satisfies all the properties associated with linear maps).