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On the Non-Symmetric Spectra of Certain Graphs
Hill, Owen
Hill, Owen
Abstract
The study of eigenvalue list multiplicities of matrices with certain graphs has appeared in volumes for symmetric real matrices. Very interesting properties, such as interlacing, equivalent geometric and algebraic multiplicities of eigenvalues, and "Parter-Weiner-Etc. Theory" drive the study of symmetric real matrices. We diverge from this and analyze non-symmetric real matrices and ask if we can attain more possible eigenvalue list multiplicities. We fully describe the possible algebraic list multiplicities for matrices with graphs $P_n, S_n, K_n$ and $K_n-K_m$.
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2015-05-01
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Mathematics