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Elements of Linear Algebra
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2-dimensional 2-electron According AiA2 angular momentum atomic axis basis functions basis vectors branching rules called Casimir operator Chapter character table coefficients commutation configuration contragredient contravariant coordinates corresponding coupling covariant tensor CR's defined denote dimension direct product double group eigenfunctions eigenvalue electrons energy levels equation example we consider finite group follows form a basis FP expansion fractional parentage given group manifold group theoretical Hamermesh Hamiltonian integer IR's irreducible representations Judd label Lie group linear space matrix elements matrix representation mixed tensor molecular symmetry groups molecule multiplets natural IO's obtain orbitals order energy orthonormal outer product parameter partitions permutational symmetry quantum chemistry quantum mechanical rank reduction respectively result rotation scalar product shown simple Lie algebras spanned spherical harmonics spin functions standard basis standard tableaux SU(M subgroup symbol symmetry transformation tensor components theorem theory tions totally antisymmetric unimodular unitary vector space write zeroth order