Orthogonality
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.
Example (
):
Let
![$ x=[1,1]$](http://www.dsprelated.com/josimages_new/mdft/img854.png)
and
![$ y=[1,-1]$](http://www.dsprelated.com/josimages_new/mdft/img855.png)
, as shown in Fig.
5.8.
Figure 5.8:
Example of two orthogonal
vectors for
.
![\includegraphics[scale=0.7]{eps/ip}](http://www.dsprelated.com/josimages_new/mdft/img856.png) |
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.
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