How to project a mxn matrix (m features, n samples) onto a space generated by a mxk matrix (m features, k factors)?

I got two matrices A and B, the dimension of A is m x n, where n represents the number of samples, and m represents the number of features. Then after dimensionality reduction, e.g., by NMF, I got B, of which the dimension is m x k, where the m features are the same in A, and k is the number of factors or new basis.

I want to project A onto B to get each sample’s weights on each factor (A = B X C). Previously I obtained weights (C) by linear regression, which aims to reconstruct A. I am wondering if there are any other ways to get the weights because sometimes the linear regression does not work well.

I also tried to get the C by C = A X B, or by calculating similarities between n samples and k factors. I’d like to know whether the above two strategies are reasonable or not?