In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible group representations, and whose columns correspond to classes of group elements. The entries consist of characters, the trace of the matrices representing group elements of the column's class in the given row's group representation.
In chemistry, crystallography, and spectroscopy, character tables of point groups are used to classify e.g. molecular vibrations according to their symmetry, and to predict whether a transition between two states is forbidden for symmetry reasons.
Read more about Character Table: Definition and Example, Orthogonality Relations, Properties, Outer Automorphisms
Famous quotes containing the words character and/or table:
“I prize the purity of his character as highly as I do that of hers. As a moral being, whatever it is morally wrong for her to do, it is morally wrong for him to do. The fallacious doctrine of male and female virtues has well nigh ruined all that is morally great and lovely in his character: he has been quite as deep a sufferer by it as woman, though mostly in different respects and by other processes.”
—Angelina Grimké (1805–1879)
“For the elemental creatures go
About my table to and fro,
That hurry from unmeasured mind
To rant and rage in flood and wind....
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—William Butler Yeats (1865–1939)