View vectors in Rⁿ as n x 1 matrices. For u and v in Rⁿ, the matrix product u^t v is a 1 x 1 matrix, called the scalar product, or inner product, of u and v. It is usually written as a single real number without brackets. The matrix product uv is an n x n matrix, called the outer product of u and v. The products u^Tv and uv^T will appear later in the text.

If u and v are in Rⁿ, how are u^Tv and v^Tu related? How are uv^T and vu^T related?