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Orthogonal

Originally, orthogonality indicates that two objects form a right angle with respect to each other. It is indicated by placing the ⊥ symbol between the objects.

 


Explanation

Nowadays, we also speak of orthogonal objects when referring to a certain property of these objects.

 


Example 1

In Euclidean geometry, you talk about lines or planes that are perpendicular to each other if they make a 90° angle with each other.

 


Example 2

The sine and cosine are orthogonal functions. The cosine is the first coordinate on the unit circle, and the sine is the second coordinate.

 


Example 3

In the Lie group SO(2), the O represents a group of rotations in which orthogonality is preserved.

 


Example 4

Modulation techniques used in 4G and 5G cell phone networks are based on the orthogonality of the many subcarriers (from several hundred to several thousand) making up the signal.

 


History

The Greek mathematician Euclid described right angles in the book Elements in 300 BC.


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