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Questions about matrix decompositions, such as the LU, Cholesky, SVD (Singular value decomposition) and eigenvalue-eigenvector decomposition.

In linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.

• For instance, when solving a system of linear equations $$Ax=b$$, the matrix $$A$$ can be decomposed via the LU decomposition. The LU decomposition factorizes a matrix into a lower triangular matrix L and an upper triangular matrix U.

• Similarly, the QR decomposition expresses $$A$$ as QR with Q an orthogonal matrix and R an upper triangular matrix.

Other decomposition techniques include: Block LU decomposition, LU reduction, rank factorisation, Cholesky decomposition, etc.

Source: Wikipedia.