### Orthogonality

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.

**Example ():**

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.

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The Pythagorean Theorem in N-Space

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Vector Cosine