The vectors (signals) and 5.11are said to be orthogonal if , denoted . That is to say
Note that if and are real and orthogonal, the cosine of the angle between them is zero. In plane geometry (), the angle between two perpendicular lines is , and , as expected. More generally, orthogonality corresponds to the fact that two vectors in -space intersect at a right angle and are thus perpendicular geometrically.
Let and , as shown in Fig.5.8.
The inner product is . This shows that the vectors are orthogonal. As marked in the figure, the lines intersect at a right angle and are therefore perpendicular.