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.

Let

Compute u^T v, v^T u, uv^T, and vu^T.

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U= -2 3 -4 نرا and v= a b C