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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

Irreducible Representation Lorentz Transformation Lorentz Group Infinitesimal Generator Rotation Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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