Linear Algebra and Group Representations: Linear algebra and introduction to group representations |
Contents
Introduction | 1 |
Contents of Volume II | 6 |
symmetric tensor algebra 369 | 13 |
Copyright | |
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A₁ adjoint AEL(V affine subspaces algebraically closed antilinear automorphism B₁ BEL(V bijective bilinear form C₂ canonical form carrier space char F commute completely reducible complex vector space conjugate corresponding coset decomposition defined denote diagonalizable dimension dimensional direct sum dual dyad e₁ e₂ eigenvalues elements equation equivalent Euclidean space exercise exists F-representation field F finite follows G-space geometry given group G group representations hence hermitian Hilbert space homomorphism intertwining invariant subspace irreducible representations isometry isotropic linear map linear operator linearly independent matrix metrical minimal polynomial Minkowski space multiplication n-dimensional non-degenerate non-singular non-zero null vector O-geometry orthogonal orthonormal basis P₁ pair perpendicular projection plane Proof properties prove quotient quotient space real vector space remark representation of G respect restriction result satisfies scalar product space self-adjoint sesquilinear subgroup subrepresentation Suppose symmetric symplectic theorem unitary V₁ V₂ zero