Randomized SVD: Catching the Top Directions

Here is a large matrix, seen through its singular values: the back row of bars, falling from left to right. We want its top five singular directions, without computing the full SVD.

Randomized SVD multiplies A by a few random vectors: k plus p of them, five plus five oversampling. Every column of A times omega is a random mixture of the columns of A.

The rest of the narration is in the book's Companion.