Hessenberg decomposition of matrix fields and bounded operator fields - Mathematics > Spectral TheoryReport as inadecuate




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Abstract: Hessenberg decomposition is the basic tool used in computational linearalgebra to approximate the eigenvalues of a matrix. In this article, wegeneralize Hessenberg decomposition to continuous matrix fields overtopological spaces. This works in great generality: the space is only requiredto be normal and to have finite covering dimension. As applications, we derivesome new structure results on self-adjoint matrix fields, we establish someeigenvalue separation results, and we generalize to all finite-dimensionalnormal spaces a classical result on trivial summands of vector bundles.Finally, we develop a variant of Hessenberg decomposition for fields of boundedoperators on a separable, infinite-dimensional Hilbert space.



Author: Benoit Jacob

Source: https://arxiv.org/



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