Pascal matrix

Definition The Pascal matrixMathworldPlanetmath P of order n is the real square n×n matrix whose entries are [1]


For n=5,


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

Pascal matrices are ill-conditioned. However, the inversePlanetmathPlanetmath of the n×n Pascal matrix is known explicitly and given in [1]. The characteristic polynomialMathworldPlanetmathPlanetmath of a Pascal triangle is a reciprocal polynomial [1].


  • 1 N.J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM, 2002.
Title Pascal matrix
Canonical name PascalMatrix
Date of creation 2013-03-22 13:44:54
Last modified on 2013-03-22 13:44:54
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 6
Author bbukh (348)
Entry type Definition
Classification msc 65F35
Classification msc 15A12
Classification msc 15A09
Classification msc 15A57