| Summary: | 碩士 === 國立高雄師範大學 === 數學系 === 106 === In this study, we want to explore whether the loss of orthogonality affects the findings of eigenvalues using basic QR method. We first introduce Norms of Vector and Matrix and Bauer-Fike theorem. Then we explain Power Method and three kind methods of QR decomposition: Gram-Schmidt process, Givens rotations, Householder transformations. Finally, we use the Hilbert matrix to observe the orthogonality obtained by the above method, and to check whether the eigenvalues are affected by the loss of orthogonality.
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