Vandermonde matrix
In linear algebra, a Vandermonde matrix is a matrix with a geometric progression in each column, i.e;
Vandermonde matrices are named after Alexandre-Théophile Vandermonde.
In mathematical terms:
These matrices are useful in polynomial interpolation, since solving an equation for , is equivalent to finding the coefficients of a polynomial that has values at .
The determinant of an Vandermonde matrix can be expressed as follows:
If two or more exponents are equal, the rank of the matrix drops (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
