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title: Orthogonality
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## Orthogonality

In mathematics and linear algebra, two vectors u and v are said to be orthogonal when their dot product is 0:  
![dot product](http://mathworld.wolfram.com/images/equations/OrthogonalVectors/Inline3.gif)  
Orthogonality can be thought of as <a href = "http://mathworld.wolfram.com/Perpendicular.html">perpendicularity</a> generalized to higher dimensional vector spaces, since the two are the same- they imply that a right angle is formed by the line, plane, or vector. 

![right angle](http://mathworld.wolfram.com/images/eps-gif/Perpendicular_1000.gif)

The following are all examples of orthogonality: 
1. If two vectors are perpendicular, that is, they meet or intersect at a right (90 degree) angle, they are orthogonal. 
2. Two vectors are orthogonal if their inner product (dot product) is equal to 0. 
3. Two vector subspaces A and B in V are orthogonal if every vector in V is orthogonal to every vector in B. 

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#### More Information:
1. http://mathworld.wolfram.com/Orthogonal.html
2. http://mathworld.wolfram.com/Perpendicular.html
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