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)
“When you got to the table you couldn’t go right to eating, but you had to wait for the widow to tuck down her head and grumble a little over the victuals, though there warn’t really anything the matter with them. That is, nothing only everything was cooked by itself. In a barrel of odds and ends it is different; things get mixed up, and the juice kind of swaps around, and the things go better.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)