# Vector Spaces

## Operations on Vectors in Euclidean Space

In this section, let be -dimensional Euclidean space and let be elements of .
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Definition:
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Inner Product
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In one sense, the inner product measures how alike or parallel two vectors are.

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Definition:
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Norm
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of a vector

The norm measures the length of a vector. The norm satisfies the two inequalities

**
Definition:
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Angle
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between two vectors

Two vectors are

*orthogonal*if .

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Definition:
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Unit Vector
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Definition:
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Distance
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between two vectors

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Definition:
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The set of vectors
are called
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orthonormal
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if