Abstract
It is shown that any four-dimensional real vector space with an inner product can be identified with a subspace of the product of two complex two-dimensional vector spaces. Making use of this identification, it is shown that each orthogonal transformation can be related with a pair of linear transformations acting on these two-dimensional spaces and several properties of tensors are also derived.
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© 2010 Birkhäuser Boston
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del Castillo, G.F.T. (2010). Spinor Algebra. In: Spinors in Four-Dimensional Spaces. Progress in Mathematical Physics, vol 59. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4984-5_1
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DOI: https://doi.org/10.1007/978-0-8176-4984-5_1
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Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4983-8
Online ISBN: 978-0-8176-4984-5
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