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.
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References
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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)
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Pallavi Sudhir, A. On the Determinant-like Function and the Vector Determinant. Adv. Appl. Clifford Algebras 24, 805–807 (2014). https://doi.org/10.1007/s00006-014-0455-3
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DOI: https://doi.org/10.1007/s00006-014-0455-3
Keywords
- Linear algebra
- clifford algebra
- exterior algebra