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:
“The first thing to be done by a biographer in estimating character is to examine the stubs of his victim’s cheque-books.”
—Silas Weir Mitchell (1829–1914)
“Will you greet your doom
As final; set him loaves and wine; knowing
The game is finished when he plays his ace,
And overturn the table and go into the next room?”
—Philip Larkin (1922–1986)