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:
Vandermonde matrices were named after Alexandre-Théophile Vandermonde (1735
), a French mathematician and musician.