View vectors in set of real numbers r superscript nℝn as ntimes×1 matrices. for u and v in set of real numbers r superscript nℝn, the matrix product bold u superscript upper t baseline bold vutv is a 1times×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 bold u bold v superscript upper tuvt is an ntimes×n matrix, called the outer product of u and v. let uequals