linalg(deprecated)
cholesky
Cholesky decomposition of a matrix
Calling Sequence
Parameters
Description
Examples
cholesky(A)
A
-
square, positive definite matrix
Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[LUDecomposition], instead.
- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.
The routine cholesky computes the cholesky decomposition of the matrix A.
The result is a lower triangular matrix R such that RtransposeR=A.
This decomposition assumes the matrix A is positive-definite. I.e. R exists with real elements on the diagonal. cholesky will fail with an error when called on a demonstrably non-positive-definite matrix.
detA=∏i=1nRi,i2.
The command with(linalg,cholesky) allows the use of the abbreviated form of this command.
withlinalg:
S≔matrix3,3,1,2,3,0,1,1,0,0,4
S≔123011004
A≔evalmtransposeS&*S
A≔1232573726
R≔choleskyA
R≔100210314
See Also
linalg(deprecated)[definite]
LinearAlgebra
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