What is “linear projection” in convolutional neural network

Question

I am reading through Residual learning, and I have a question. What is "linear projection" mentioned in 3.2? Looks pretty simple once got this but could not get th

Answer 1

A linear projection is one where each new feature is simple a weighted sum of the original features. As in the paper, this can be represented by matrix multiplication. if x is the vector of N input features and W is an M-byN matrix, then the matrix product Wx yields M new features where each one is a linear projection of x. Each row of W is a set of weights that defines one of the M linear projections (i.e., each row of W contains the coefficients for one of the weighted sums of x).