Assuming that a LU decomposition exists for all desired submatrices of a matrix `a`

, is there an easy way to extract the decomposition for the submatrix from the decomposition of `a`

? It is easy in this example:

```
julia> using LinearAlgebra
julia> a = randn(10,10);
julia> a2 = a[1:5,1:5];
julia> P = lu(a, NoPivot());
julia> P2 = lu(a2, NoPivot());
julia> P.factors[1:5,1:5] ≈ P2.factors
true
```

In that way I can compute the decomposition of the large matrix `a`

once and then simply view the decomposition for each desired submatrix.

My question is: Can I do the same when I do not want the submatrix with indices `1:n`

, but arbitrary subindices. It would be good also, I guess, if `NoPivot()`

is not a requirement. And most importantly: can I do this for the UMFPACK LU for sparse matrices?

Thank you for any help.