public CholeskyDecomposition CholeskyDecomposition()
Public Function CholeskyDecomposition As CholeskyDecomposition
public: CholeskyDecomposition^ CholeskyDecomposition()
member CholeskyDecomposition : unit -> CholeskyDecomposition
A Cholesky decomposition is a special decomposition that is possible only for positive definite matrices. (A positive definite matrix M has xTMx > 0 for any vector x. Equivilently, M is positive definite if all its eigenvalues are positive.)
The Cholesky decomposition represents M = C CT, where C is lower-left triangular (and thus CT is upper-right triangular. It is basically an LU decomposition where the L and U factors are related by transposition. Since the M is produced by multiplying C "by itself", the matrix C is sometimes call the "square root" of M.
Cholesky decomposition is an O(N3) operation. It is about a factor of two faster than LU decomposition, so it is a faster way to obtain inverses, determinates, etc. if you know that M is positive definite.
The fastest way to test whether your matrix is positive definite is attempt a Cholesky decomposition. If this method returns null, M is not positive definite.