منابع مشابه
Enclosure Theorems for Eigenvalues of Elliptic Operators
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Proof. Suppose Mv = λv. We want to show that λ has imaginary value 0. For a complex number x = a + ib, the conjugate of x, is defined as follows: x∗ = a − ib. So, all we need to show is that λ = λ∗. The conjugate of a vector is the conjugate of all of its coordinate. Taking the conjugate transpose of both sides of the above equality, we have v∗M = λ∗v∗, (8.1) where we used that M = M . So, on o...
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Hermitian matrices have real eigenvalues. The Cauchy interlace theorem states that the eigenvalues of a Hermitian matrix A of order n are interlaced with those of any principal submatrix of order n − 1. Theorem 1 (Cauchy Interlace Theorem). Let A be a Hermitian matrix of order n, and let B be a principal submatrix of A of order n − 1. If λ n ≤ λ n−1 ≤ · · · ≤ λ 2 ≤ λ 1 lists the eigenvalues of ...
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in the area of automotive engineering there is a tendency to more electrification of power train. in this work control of an induction machine for the application of electric vehicle is investigated. through the changing operating point of the machine, adapting the rotor magnetization current seems to be useful to increase the machines efficiency. in the literature there are many approaches wh...
15 صفحه اولMy favorite application using eigenvalues: Eigenvalues and the Graham-Pollak Theorem
The famous Graham-Pollak Theorem states that one needs at least n− 1 complete bipartite subgraphs to partition the edge set of the complete graph on n vertices. Originally proved in conjunction with addressing for networking problems, this theorem is also related to perfect hashing and various questions about communication complexity. Since it’s original proof using Sylvester’s Law of Intertia,...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1961
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1961-10658-7