Abstract
This chapter refreshes such necessary algebraic knowledge as will be needed in this book. It introduces function spaces, the meaning of a linear operator, and the properties of unitary matrices. The homomorphism between operations and matrix multiplications is established, and the Dirac notation for function spaces is defined. For those who might wonder why the linearity of operators need be considered, the final section introduces time reversal, which is anti-linear.
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References
Dirac, P.A.M.: The Principles of Quantum Mechanics. Clarendon Press, Oxford (1958)
Altmann, S.L.: Rotations, Quaternions, and Double Groups. Clarendon Press, Oxford (1986)
Wigner, E.P.: Group Theory. Academic Press, New York (1959)
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© 2013 Springer Science+Business Media Dordrecht
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Ceulemans, A.J. (2013). Function Spaces and Matrices. In: Group Theory Applied to Chemistry. Theoretical Chemistry and Computational Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6863-5_2
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DOI: https://doi.org/10.1007/978-94-007-6863-5_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-6862-8
Online ISBN: 978-94-007-6863-5
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