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Advances in Applied Clifford Algebras

, Volume 24, Issue 3, pp 805–807 | Cite as

On the Determinant-like Function and the Vector Determinant

  • Abhimanyu Pallavi Sudhir
Article
  • 105 Downloads

Abstract

A generalisation of the determinant to rectangular matrices, known as the determinant-like function, has its magnitude defined previously. In this paper, we show that the determinant-like function is a rotation of the vector determinant.We further propose that this rotation is an identity transformation and thus the determinant-like function is in fact the same as the vector determinant. From this, we derive some properties of the determinant-like function.

Keywords

Linear algebra clifford algebra exterior algebra 

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References

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    H. Pyle: Non-Square Determinants and Multilinear Vectors. Mathematics Association of America 35(2), 65–69 (1962)zbMATHGoogle Scholar
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    M. Radic, A Definition of Determinant of Rectangular Matrix, 1(21) (1966), 321–349Google Scholar
  3. 3.
    A. Pallavi Sudhir: Defining the determinant-like function for m by n matrices using the Exterior Algebra. Advances in Applied Clifford Algebras 23(4), 787–792 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Dhirubhai Ambani International SchoolBombayIndia

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