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 legislator should direct his attention above all to the education of youth; for the neglect of education does harm to the constitution. The citizen should be molded to suit the form of government under which he lives. For each government has a peculiar character which originally formed and which continues to preserve it. The character of democracy creates democracy, and the character of oligarchy creates oligarchy.”
—Aristotle (384–323 B.C.)
“The salt person and blasted place
I furnish with the meat of a fable;
If the dead starve, their stomachs turn to tumble
An upright man in the antipodes
Or spray-based and rock-chested sea:
Over the past table I repeat this present grace.”
—Dylan Thomas (1914–1953)