In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an matrix
with entries , the jth power of the number , for all zero-based indices and .[1] Some authors define the Vandermonde matrix as the transpose of the above matrix.[2][3]
The determinant of a square Vandermonde matrix (when ) is called a Vandermonde determinant or Vandermonde polynomial. Its value is:
This is non-zero if and only if all are distinct (no two are equal), making the Vandermonde matrix invertible.
^Roger A. Horn and Charles R. Johnson (1991), Topics in matrix analysis, Cambridge University Press. See Section 6.1.
^Golub, Gene H.; Van Loan, Charles F. (2013). Matrix Computations (4th ed.). The Johns Hopkins University Press. pp. 203–207. ISBN 978-1-4214-0859-0.
^Cite error: The named reference MS was invoked but never defined (see the help page).
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