Editing Character table (section)

{{Short description|Two-dimensional group theory table}}
In [[group theory]], a branch of [[abstract algebra]], a '''character table''' is a two-dimensional table whose rows correspond to [[irreducible representation]]s, and whose columns correspond to [[conjugacy class]]es of [[group (mathematics)|group]] elements.  The entries consist of [[character theory|characters]], the [[trace (linear algebra)|trace]]s of the [[matrix (mathematics)|matrices]] representing group elements of the column's class in the given row's group representation. In [[chemistry]], [[crystallography]], and [[spectroscopy]], [[List of character tables for chemically important 3D point groups|character tables of point groups]] are used to classify ''e.g.'' [[molecule|molecular]] vibrations according to their symmetry, and to predict whether a transition between two states is forbidden for symmetry reasons. Many university level textbooks on [[physical chemistry]], [[quantum chemistry]], [[spectroscopy]] and [[inorganic chemistry]] devote a chapter to the use of symmetry group character tables.<ref>''Quantum Chemistry'', 3rd ed. John P. Lowe, Kirk Peterson {{ISBN|0-12-457551-X}}</ref><ref>''Physical Chemistry: A Molecular Approach'' by Donald A. McQuarrie, John D. Simon {{ISBN|0-935702-99-7}}</ref><ref>''The chemical bond'', 2nd ed. J.N. Murrell, S.F.A. Kettle, J.M. Tedder {{ISBN|0-471-90760-X}}</ref><ref>''Physical Chemistry'', 8th ed. P.W. Atkins and J. de Paula, W.H. Freeman, 2006 {{ISBN|0-7167-8759-8}}, chap.12</ref><ref>P. R. Bunker and Per Jensen (1998), ''Molecular Symmetry and Spectroscopy'', 2nd ed. , NRC Research Press,Ottawa {{ISBN|9780660196282}}[https://volumesdirect.com/products/molecular-symmetry-and-spectroscopy?_pos=1&_sid=ed0cc0319&_ss=r]</ref><ref>G. L. Miessler and D. A. Tarr ''Inorganic Chemistry'', 2nd ed. Pearson, Prentice Hall, 1998 {{ISBN|0-13-841891-8}}, chap.4.</ref><!--each book needs date and chapter/page range-->