As an example, consider the simple case of a matrix multiplication between a m × n matrix M and a n × 1 vector − → v .
matrix m can be seen as a list of column vectors The result of the matrix multiplication is a combination of scalar multiplications of each element v i of the vector − → v with the corresponding column vector − → w i of the matrix m. we have: By denoting v i a feature whenever it is non-zero, we obtain an equivalent form as follows: The above notation says that we collect features of each − → w i vector but only up to "featureness" of v i , that is up to v i being non-zero.