When describing the matrix form for the change of basis, my book says that the matrix you construct from the basis vectors is by taking the complex conjugate of each basis vector and turning that into a row. Then to get the new coordinates you just do $$ M\vec{x}=\vec{y}$$
I seem to recall in previous classes that you construct a matrix where each column is a basis vector and then do $$ M^H \vec{x} = \vec{y}$$
Is the first or second more typical in convention. Is the convention different for discrete signal processing than for just math?