Spectral properties of random non-self-adjoint matrices and operators
نویسندگان
چکیده
منابع مشابه
Spectral Properties of Random Non-self-adjoint Matrices and Operators
We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically uncomputable for similar matrices of a larger size. We also describe a stochastic family of bounded operators in infinite dimensions for almost all of which the ...
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This agrees with the definition of the spectrum in the matrix case, where the resolvent set comprises all complex numbers that are not eigenvalues. In terms of its spectrum, we will see that a compact operator behaves like a matrix, in the sense that its spectrum is the union of all of its eigenvalues and 0. We begin with the eigenspaces of a compact operator. We start with two lemmas that we w...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
سال: 2001
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2000.0662