Vandermonde matrix

In this post, we will compute a classical determinant called the Vandermonde determinant. Though the computation of this determinant looks intractable at first, there turns out to be a beautiful formula for it, with a very neat proof. Somewhat surprisingly, the matrices involved and this result are related to the notion of Lagrange interpolating polynomials. … Continue reading Vandermonde matrix

Polynomials

Polynomials are probably the most usual types of functions out there, because they do not need any heavy machinery to be introduced: all one needs to know is how to add and multiply numbers. This alone justifies a discussion of polynomials. However, seeing polynomials as merely "simple functions" is reductive, and indeed, a more abstract … Continue reading Polynomials