What is a Vandermonde matrix?
In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row, i.e., an m × n matrix for all indices i and j. The identical term Vandermonde matrix was used for the transpose of the above matrix by Macon and Spitzbart (1958).
Who is Alexander Vandermonde?
Alexandre-Théophile Vandermonde (28 February 1735 – 1 January 1796) was a French mathematician, musician and chemist who worked with Bézout and Lavoisier; his name is now principally associated with determinant theory in mathematics. He was born in Paris, and died there.
What did Alexandre Théophile do for a living?
Alexandre-Théophile was awarded his bachelier on 7 September 1755 and his licencie on 7 September 1757. His first love was music and his instrument was the violin. He pursued a music career and he only turned to mathematics when he was 35 years old.
What is an alternating function in a Vandermonde matrix?
For example, take a Vandermonde matrix with the variables . We can define a function det. Now if we transpose any two variables and we have simply switched two rows of the matrix. It follows that is an alternating function. The proof of Proposition 1 is a direct consequence of the following lemma.
Proposition 2 Given a set of elements , a Vandermonde matrix is an matrix where the column is the vectorfor . A formula for the determinant of follows: In particular, if are pairwise disjoint, the determinant is nonzero.
How do you find the Vandermonde matrix in Python?
A = vander (v) returns the Vandermonde Matrix such that its columns are powers of the vector v. Use the colon operator to create vector v. Find the Vandermonde matrix for v. Find the alternate form of the Vandermonde matrix using fliplr. Input, specified as a numeric vector.
What is Corollary 2 in Vandermonde matrix?
Corollary 2 Given a set of distinct elements , and the Vandermonde matrix with second column equal to , the determinant det. The Vandermonde matrix plays an important role when proving certain bounds on the distances of cyclic codes.