MATLAB Function Reference

pascal

Pascal matrix

Syntax

• A = pascal(n)
  A = pascal(n,1)
  A = pascal(n,2)
  

Description

A = pascal(n) returns the Pascal matrix of order n: a symmetric positive definite matrix with integer entries taken from Pascal's triangle. The inverse of A has integer entries.

A = pascal(n,1) returns the lower triangular Cholesky factor (up to the signs of the columns) of the Pascal matrix. It is involutary, that is, it is its own inverse.

A = pascal(n,2) returns a transposed and permuted version of pascal(n,1). A is a cube root of the identity matrix.

Examples

pascal(4) returns

• 1     1     1     1
  1     2     3     4
  1     3     6    10
  1     4    10    20
  

A = pascal(3,2) produces

• A =
       1     1     1
      -2    -1     0
       1     0     0
  

See Also

chol

partialpath

patch