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Matlab[chol] - compute the Cholesky factorization of a MapleMatrix or MatlabMatrix in MATLAB(R), where R'*R = X, and P is nonzero only if X is positive definite
Calling Sequence
chol(X)
chol(X, output=R)
chol(X, output=RP)
Parameters
X
-
square MapleMatrix, or MatlabMatrix
output
specify the form of the output (optional)
R
return only unitary Q matrix
RP
return Q and upper decomposed R matrix
Description
The commands Matlab[chol](X) and Matlab[chol](X, 'output'='R') use MATLAB to compute the Cholesky factorization, R, of a MapleMatrix or MatlabMatrix, where transpose(R)*(R) = X. If X is not positive definite, then an error is returned.
When you specify the optional parameter, , two values are returned. The second value, P, is zero if X is positive definite; otherwise, P is 1+dimension(R). The first value, R, is the largest dimension matrix such that transpose(R)*(R) = XX, where XX is the upper left corner of X, of dimension P.
For further details on the chol command, see the MATLAB documentation.
Examples
Define the Maple matrix
Compute the factorization
[1. 0. ]
[ ]
[0. 1.73205080756887720]
An example of the RP option
[1.73205080756887720 0.577350269189625842 1.73205080756887742]
r, p := [ 0. 2.38047614284761665 1.26025207562520891], 4.
[ 0. 0. 1.84709629036559763]
See Also
LinearAlgebra[MatrixInverse], Matlab, Matlab[det], Matlab[evalM], Matlab[inv], MatlabMatrix
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