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Preliminaries Matrices Determinants Polynomials
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according to Theorem adjoint affine bijective bilinear form called cardinality Cauchy sequence Chapter char(F characteristic polynomial complete complex inner product converges coset cyclic submodules defined Definition Let denoted diagonal dim(V dimension direct sum eigenvalues eigenvectors element elementary divisors equivalent Example exists field F following theorem free module Hence Hilbert basis Hilbert space hyperbolic identity implies infinite inner product space invariant isometry isomorphism theorem ker(p Let r G linear combination linear functional linear operator linear transformation linearly independent linearly independent set matrix maximal metric space metric vector space minimal polynomial Moreover mT(x nonempty nonnegative nonsingular ordered basis orthogonal geometry orthogonal projection orthogonally diagonalizable orthonormal basis orthonormal set principal ideal domain Proof Prove quotient space R-module rational canonical form rfim(V scalar multiplication self-adjoint Sheffer space over F spanning set submodule subset subspace suppose surjective symmetric tensor product unitary vector space