Vandermonde matrix
In
linear algebra, a
Vandermonde matrix is a
matrix with a
geometric progression in each column, i.e;
In mathematical terms:
These matrices are useful in
polynomial interpolation, since solving an equation for , is equivalent to finding the coefficents of a polynomial that has values at .
The determinant of a square Vandermonde matrix of a dimension can be expressed as follows:
If two or more exponents are equal, the rank of the matrix decreases (if all are distinct, then is of full rank). This problem can alleviated by using a generalisation called confluent Vandermonde matrices, where the
k-multiple columns are replaced by:
- where
Vandermonde matrices were named after Alexandre-Théophile Vandermonde (
1735-
1796), a French mathematician and musician.