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- W2497753755 abstract "This chapter discusses the way in which the eigenvalues and eigenvectors of a matrix A vary as functions of the elements aij of A. Rouche's theorem states that if it is assumed that f and g are analytic and single valued in a domain D and on its boundary , and that on , |f(z) — g(z)| < |f(z) |, then f and g have exactly the same number of zeros in D. According to continuity of roots theorem if p be the polynomial with real or complex coefficients a0, an-1 and with roots λ1, … λn, then for any sufficiently small ɛ > 0, there is a δ > 0 such that the roots μi of any polynomial q (λ) = λn +bn-1 λn-1 +… + b0 with |bi − ai | ≤ δ, i = 0… n−1, can be ordered so that |λi −μi| ≤ ɛ, i = 1, …, n." @default.
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- W2497753755 date "1972-01-01" @default.
- W2497753755 modified "2023-09-27" @default.
- W2497753755 title "EIGENVALUES AND EIGENVECTORS" @default.
- W2497753755 doi "https://doi.org/10.1016/b978-0-12-528560-5.50011-4" @default.
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