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# Vector Spaces

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Review  :: Operations ::  Geometric Representation

## Operations on Vectors in Euclidean Space

In this section, let be -dimensional Euclidean space and let be elements of .

Definition: Inner Product

In one sense, the inner product measures how alike or parallel two vectors are.

Definition: Norm of a vector

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

Definition: Angle between two vectors

Two vectors are orthogonal if .

Definition: Unit Vector

Definition: Distance between two vectors

Definition: The set of vectors are called orthonormal if

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 29). Vector Spaces. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Communication_Systems_I_1/vectors_spaces_2.htm. This work is licensed under a Creative Commons License