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

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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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     title = {An {Elementary} {Proof} of the {Exponential} {Conditioning} of {Real} {Vandermonde} {Matrices}},
     journal = {Bollettino della Unione matematica italiana},
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     zbl = {1139.15002},
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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/