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Chapter 4 Euclidean Vector Spaces

4.1 Euclidean n-Space. . Definition Vectors in n-Space. If n is a positive integer, then an ordered n-tuple is a sequence of n real numbers (a1,a2,,an).. The set of all ordered n-tuple is called n-space and is denoted by Rn. Definition . Two vectors u=(u1 ,u2 ,,un) and v=(v1 ,v2 ,, vn) in Rn are

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Chapter 4 Euclidean Vector Spaces

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    1. Chapter 4 Euclidean Vector Spaces 4.1 Euclidean n-Space 4.2 Linear Transformations from Rn to Rm 4.3 Properties of Linear Transformations Rn to Rm

    2. 4.1 Euclidean n-Space

    3. Definition Vectors in n-Space If n is a positive integer, then an ordered n-tuple is a sequence of n real numbers (a1,a2,,an).. The set of all ordered n-tuple is called n-space and is denoted by Rn

    4. Definition Two vectors u=(u1 ,u2 ,,un) and v=(v1 ,v2 ,, vn) in Rn are called equal if The sum u+v is defined by and if k is any scalar, the scalar multiple ku is defined by

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