Pascal matrix

Definition The Pascal matrix $P$ of order $n$ is the realsquare $n\times n$ matrix whose entries are [1]

$$P_{ij}=\left(\genfrac{}{}{0pt}{}{i+j-2}{j-1}\right).$$

For $n=5$,

so we see that the Pascal matrix contains the Pascal triangle on its antidiagonals.

Pascal matrices are ill-conditioned. However, the inverse of the$n\times n$ Pascal matrix is known explicitly and given in [1].The characteristic polynomial of a Pascal triangle is a reciprocalpolynomial [1].