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Alternant matrix

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A square matrix of the general form $\left({f_i(x_j)}\right)$ where the $x_j$ are variables and the $f_i({\cdot})$ are functions, $i,j$ ranging over $1,\ldots,n$. An alternant is the determinant of such a matrix. A common use of the term is when the $f_i({\cdot})$ are powers, so that the general entry is ${x_j}^{\lambda_i}$ for exponents $\lambda_i$, and especially the case $\lambda_i = i-1$ for $i = 1,\ldots,n$, when the alternant is a Vandermonde determinant.

References

  • Thomas Muir. A treatise on the theory of determinants. Dover Publications (1960) [1933]
How to Cite This Entry:
Alternant matrix. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Alternant_matrix&oldid=37542