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Determinants and multiplicative functionals on quaternion matrices

✍ Scribed by Jiangnan Fan

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
92 KB
Volume
369
Category
Article
ISSN
0024-3795

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✦ Synopsis

Determinants of matrices over a field are multiplicative. Does there exist an extension of the definition of determinants of real matrices to quaternion matrices, such that the multiplication theorem holds? This paper proves there does not exist such an extension. We give a universal property on multiplicative functionals from the set of quaternion matrices to the set of quaternion numbers. The theorem tells us, in a sense, the definition of determinants for quaternion matrices is unique.

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