matrix-decomposition-website

What's matrix-decomposition-website?

• provide a caculator for decompose matrix using 2 method is cholesky and LDL

What's cholesky and LDL decomposition?

• Cholesky decomposition is matrix factorization technique, especially valuable for positive definite matrices. It factorizes the matrix into the product of a lower triangular matrix (L) and its conjugate transpose (L^H), where L^H represents the Hermitian transpose of L
• LDL decomposition is a fundamental technique in linear algebra that factorizes a symmetric matrix into the product of a lower triangular matrix (L), a diagonal matrix (D), and the transpose of L
• Both method can only decompose matrix squared, symmetric, however Cholesky can only apply to positive definite matrix

How are classes of decomposition structured?

MatrixDecomposition

• is configured with a decompositor object
• maintain a reference to a Strategy object

Decompositor

• declare an abstract class, MatrixDecomposition uses this abstract class to call the algorithm defined by a stategy which is CholeskyDecompositor & LdlDecompositor
• define decompose() - skeleton of an algorithm, deferring findFactor() steps for subclasses

concrete stategy ( CholeskyDecompositor & LdlDecompositor )

• implements findFactor() method that proper for its algorithm