unitary group

English

Noun

unitary group (plural unitary groups)

1. (group theory) For given n, the group of n×n unitary matrices, with the group operation of matrix multiplication.
   • 1995, Ruben Pauncz, The Symmetric Group in Quantum Chemistry, CRC Press, page 195:

     The symmetric group is closely related to the unitary group. […] The latest developments in spin free quantum chemistry have been the use of the unitary group for the calculation of the matrix elements of the Hamiltonian in the configuration interaction treatment.

   • 2004, [1999], Shoon K. Kim, Group Theoretical Methods and Applications to Molecules and Crystals, Cambridge University Press, page 53:

     Two of the most important types of groups that occur in physics are unitary groups and orthogonal groups.

Usage notes

The unitary group of degree n is a subgroup of the general linear group GL(n, C) (i.e., the underlying field is that of the complex numbers) and can be denoted U(n) or U_n.

Synonyms

• hyperorthogonal group (especially over finite fields, obsolete)

Hyponyms

• circle group

Derived terms

• co-unitary group
• projective unitary group
• special unitary group
• general unitary group

Translations

group of n×n unitary matrices

• Finnish: unitaarinen ryhmä
• German: unitäre Gruppe f