Geodesic
An Elementary Proof of the Exponential Conditioning of Real Vandermonde Matrices
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 761-768 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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We provide and discuss an elementary proof of the exponential con- ditioning of real Vandermonde matrices which can be easily given in undergraduate courses: we exclusively use the definition of conditioning and the sup-norm formula on $[-1, 1]$ for Chebyshev polynomials of first kind. The same proof idea works virtually unchanged for the famous Hilbert matrix. 
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     author = {Serra Capizzano, Stefano},
     title = {An {Elementary} {Proof} of the {Exponential} {Conditioning} of {Real} {Vandermonde} {Matrices}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {761--768},
     year = {2007},
     volume = {Ser. 8, 10B},
     number = {3},
     zbl = {1139.15002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a20/}
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Serra Capizzano, Stefano. An Elementary Proof of the Exponential Conditioning of Real Vandermonde Matrices. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 761-768. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a20/