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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

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