MATLAB Function Reference Volume 1: A - E - Bad Request

chol
2chol
Purpose Cholesky factorization
Syntax R = chol(X)
[R,p] = chol(X)
Description The chol function uses only the diagonal and upper triangle of X. The lower
triangular is assumed to be the (complex conjugate) transpose of the upper.
That is, X is Hermitian.
2-246
R = chol(X), where X is positive definite produces an upper triangular R so
that R'*R = X. If X is not positive definite, an error message is printed.
[R,p] = chol(X), with two output arguments, never produces an error
message. If X is positive definite, then p is 0 and R is the same as above. If X is
not positive definite, then p is a positive integer and R is an upper triangular
matrix of order q = p-1 so that R'*R = X(1:q,1:q).
Examples The binomial coefficients arranged in a symmetric array create an interesting
positive definite matrix.
n = 5;
X = pascal(n)
X =
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
It is interesting because its Cholesky factor consists of the same coefficients,
arranged in an upper triangular matrix.
R = chol(X)
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