The vectors (signals) and
^{5.11}are 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.

Figure 5.8:
Example of two orthogonal
vectors for .

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.