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:
“In my experience, persons, when they are made the subject of conversation, though with a Friend, are commonly the most prosaic and trivial of facts. The universe seems bankrupt as soon as we begin to discuss the character of individuals. Our discourse all runs to slander, and our limits grow narrower as we advance. How is it that we are impelled to treat our old Friends so ill when we obtain new ones?”
—Henry David Thoreau (1817–1862)
““A sigh for every so many breath,
And for every so many sigh a death.
That’s what I always tell my wife
Is the multiplication table of life.””
—Robert Frost (1874–1963)