Dot product of two vectors

Algebraic view

The dot product of two -dimensional column vectors is the matrix product of and :

The dot product is a special case of the Frobenius inner product. As such, it can also be expressed as .

Geometric view

Any two vectors and form an angle between them. The dot product is given as

Notice that when and are orthogonal, then and so ; when they are co-directional, and so .