The harmonic and geometric mean of vectors |
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| Authors: | W N Anderson G E Trapp |
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| Institution: |
a Department of Mathematics and Computer Science, Fairley Dickinson University, Teaneck, NJ
b Department of Statistics and Computer Science, West Virginia University, Morgantown, WV |
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| Abstract: | New vector operations are defined that generalize the classical harmonic and geometric means of scalars. The definition of the harmonic mean involves an explicit vector formula, whereas the geometric mean of two vectors is defined by an iterative procedure. Two special cases are described in some detail, the case of 2-vectors which are equivalent to the complex numbers, and the case of 4-vectors which are a representation of the quaternions. |
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