### Quick description

Factored forms for matrices (whether LU, Cholesky, QR, SVD or some other factorization) is not only convenient for solving linear equations, least squares problems, or other problems, but also helps to maintain sparsity and avoid loss of precision.

### Prerequisites

Linear algebra.

### Example 1

Avoid computing the inverse!

Computing the inverse not only destroys sparsity and takes a substantial amount of time and memory, but we lose the backward error property that makes LU factorization (and the other factorizations) particularly valuable.

### Example 2

Update a factorization rather than re-factorize.

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