A Polarization Formula for Clifford Modules

Dante M. Giarrusso; Joseph D. Romano

doi:10.1080/03081089308818257

A Polarization Formula for Clifford Modules

Dante M. Giarrusso, Joseph D. Romano

Physics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that a well-known polarization formula for Hermitian inner products on complex vector spaces generalizes to the case of inner products on Clifford modules. This observation allows us to conclude that norm-preserving linear maps of Clifford modules necessarily preserve the inner product. These results hold for modules over the quaternions as a special case.

Original language	English
Pages (from-to)	191-194
Number of pages	4
Journal	Linear and Multilinear Algebra
Volume	35
Issue number	3-4
DOIs	https://doi.org/10.1080/03081089308818257
State	Published - Aug 1 1993

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title = "A Polarization Formula for Clifford Modules",

abstract = "We show that a well-known polarization formula for Hermitian inner products on complex vector spaces generalizes to the case of inner products on Clifford modules. This observation allows us to conclude that norm-preserving linear maps of Clifford modules necessarily preserve the inner product. These results hold for modules over the quaternions as a special case.",

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AB - We show that a well-known polarization formula for Hermitian inner products on complex vector spaces generalizes to the case of inner products on Clifford modules. This observation allows us to conclude that norm-preserving linear maps of Clifford modules necessarily preserve the inner product. These results hold for modules over the quaternions as a special case.

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