Originally Posted by

**ecotheory** Thanks, I did not mean squares of the vectors. I was thinking of the vector norms, so yes. Minimize the sum of dot products.

I should have said:

Given a set of vectors v_i = {v_1, ..., v_n} in R, describe the set of vectors in a one-dimensional subspace of R, with basis b, that minimizes the sum of squares of the norm of v_i-a_i*b, where a_i = {a_1, ..., a_n} are scalars.

The motivation for the problem is that I am seeking a method for finding a matrix with rank=1 which can be considered most "similar" to a given square matrix. In my phrasing of the problem, I have considered the rows of the matrix as vectors v. While their may be a different approach, I really would like an answer in terms of scalars a and a vector b.

Thanks for your question/clarification.