## A Geometric Proof of Convergence for the QR Method |

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assume block of order Cauchy-Schwarz inequality columns complex number computation is performed compute a unitary denote eigenvalues h F.L. BAUER functie gain all mass geldt h large Hence Hessenberg form Hessenberg matrices Hessenberg matrix hypotheses H IFIP congress 1968 infinite subset initial matrix invariant subspace inverse iteration iteration process Krylov sequences limit f linear subspaces lower diagonal block mass-center matrices A tends matrices Q method with shifts minimizing polynomial monic non-singular for h non-singular matrix normal normal matrix nullvector orthogonal complement p-dimensional subspace perform the iteration performed in complex performed in real points polynomial of degree probleem PROOF OF CONVERGENCE QR algorithm QR method quence real arithmetic real numbers section 9 sequence of linear sequence of matrices set of indices spanned strict inequality T+H2h tary matrix tend to zero Treppeniteration unitary matrix upper triangular matrix vectors x+z wiskunde zijn zodat