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

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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.",

author = "Giarrusso, {Dante M.} and Romano, {Joseph D.}",

note = "Funding Information: We would like to thank Prof. Wu-Teh Hsiang for suggesting this problem. We would also like to thank an anonymous referee for pointing out that the polarization formula simplifies when n mod 4 equals one. This research was supported in part by NSF grants PHY90-16733 and PHY91-12240.",

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AU - Romano, Joseph D.

N1 - Funding Information: We would like to thank Prof. Wu-Teh Hsiang for suggesting this problem. We would also like to thank an anonymous referee for pointing out that the polarization formula simplifies when n mod 4 equals one. This research was supported in part by NSF grants PHY90-16733 and PHY91-12240.

PY - 1993/8/1

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N2 - 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.

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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DO - 10.1080/03081089308818257

M3 - Article

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SP - 191

EP - 194

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 3-4

ER -

A Polarization Formula for Clifford Modules

Abstract

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