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

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aſh Bauer block of order Bºx BUUREMA Cauchy–Schwarz inequality columns complex number computation is performed compute a unitary Dealo denote F.L. BAUER follows Fººt Fºx functie gain all mass h large Hence Hessenberg form Hessenberg matrix hºn infinite subset initial matrix invariant subspace inverse iteration iteration process Krylov sequences lemma limit f limiting polynomial linear subspaces lower diagonal block lvº mass-center matrices A(h matrix h method with shifts minimizing polynomial monic non-singular matrix normal matrix º º orthogonal complement p-dimensional subspace performed in real polynomial of degree Pºop PROOF OF CONVERGENCE QR algorithm QR method quence real arithmetic real numbers section 9 sequence of linear sequence of matrices spanned strict inequality tary matrix tend to zero Treppeniteration unitary matrix upper triangular matrix vector verzameling Vºivºlº vºlo Vºlvºlvº wiskunde Xiºn zijn