pascal(N) is the Pascal matrix of order N: a symmetric positive definite matrix with integer entries, made up from Pascal's triangle. Its inverse has integer entries.

Generate a pascal matrix:

>> A = pascal(5)

A =

1 1 1 1 1

1 2 3 4 5

1 3 6 10 15

1 4 10 20 35

1 5 15 35 70

(Ref: wikipedia)

In linear algebra, the Cholesky decomposition or Cholesky factorization is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, useful for efficient numerical solutions and Monte Carlo simulations. It was discovered by AndrĂ©-Louis Cholesky for real matrices. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.

R =

1 1 1 1 1

0 1 2 3 4

0 0 1 3 6

0 0 0 1 4

0 0 0 0 1

Recover the matrix from its Cholesky decomposition and its transpose.

>> A1 = R' * R

A1 =

1 1 1 1 1

1 2 3 4 5

1 3 6 10 15

1 4 10 20 35

1 5 15 35 70

Generate a pascal matrix:

>> A = pascal(5)

A =

1 1 1 1 1

1 2 3 4 5

1 3 6 10 15

1 4 10 20 35

1 5 15 35 70

(Ref: wikipedia)

In linear algebra, the Cholesky decomposition or Cholesky factorization is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, useful for efficient numerical solutions and Monte Carlo simulations. It was discovered by AndrĂ©-Louis Cholesky for real matrices. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.

^{}>> R = chol(A)R =

1 1 1 1 1

0 1 2 3 4

0 0 1 3 6

0 0 0 1 4

0 0 0 0 1

Recover the matrix from its Cholesky decomposition and its transpose.

>> A1 = R' * R

A1 =

1 1 1 1 1

1 2 3 4 5

1 3 6 10 15

1 4 10 20 35

1 5 15 35 70