Lie Groups

  • Petre P. Teodorescu
  • Nicolae-Alexandru P. Nicorovici
Part of the Fundamental Theories of Physics book series (FTPH, volume 140)

Abstract

Let A be a square matrix of elements aik ∈ ℂ, i,k, = 1, 2,, n. The matrix Equation ID=EquaEquationSource Format=MATHTYPE![CDATA[% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHb3oNStNQ+fNoasaacH8srps % 0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr % 0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaci % GacaGaaeqabaWaaeaaeaqbaOqaaiaadgeadaahaaWcbeqaceaasWGa % aiiiGaaakiabg2da9iqadgeagaqeamaaCaaaleqabaGaamivaaaaki % aacYcaaaa!475B!]EquationSourceEquationSource Format=TEX![CDATA[$$[{A^dag } = {bar A^T},]$$]EquationSourceEquation where AT is the transposed of A, and A is the complex conjugate of A, is called the adjoint (or Hermitian conjugate) of the matrix A. If A = Ā then the matrix A is real, and if A = −Ā then the matrix A is pure imaginary. A square matrix S is called symmetric or skew-symmetric, if S = ST or S = −ST, respectively. A square matrix H is called Hermitian if H = H, and anti-Hermitian if H = H. Note that, a real and symmetric matrix is also Hermitian.

Keywords

Manifold Dcpd 

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Petre P. Teodorescu
    • 1
  • Nicolae-Alexandru P. Nicorovici
    • 2
  1. 1.Faculty of MathematicsUniversity of BucharestBucharestRomania
  2. 2.School of PhysicsThe University of SydneyAustralia

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