[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）12 (1002ﾚｽ)
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545(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2023/01/08(日)17:04 ID:9zXu/9tz(17/34) AAS
つづき

Applications
The Vandermonde determinant is used in the representation theory of the symmetric group.[8]

When the values αk belong to a finite field, then the Vandermonde determinant is also called a Moore determinant and has specific properties that are used, for example, in the theory of BCH code and Reed?Solomon error correction codes.

The discrete Fourier transform is defined by a specific Vandermonde matrix, the DFT matrix, where the numbers αi are chosen to be roots of unity. Using the Fast Fourier Transform it is possible to compute the product of a Vandermonde matrix with a vector in O(n(log n)^2) time.[9]

外部ﾘﾝｸ:en.wikipedia.org
Alexandre-Theophile Vandermonde (28 February 1735 ? 1 January 1796)
Biography
Vandermonde was a violinist, and became engaged with mathematics only around 1770. In Memoire sur la resolution des equations (1771) he reported on symmetric functions and solution of cyclotomic polynomials; this paper anticipated later Galois theory (see also abstract algebra for the role of Vandermonde in the genesis of group theory).
The same year he was elected to the French Academy of Sciences. Memoire sur des irrationnelles de differents ordres avec une application au cercle (1772) was on combinatorics, and Memoire sur l'elimination (1772) on the foundations of determinant theory.
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