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.