Type parameter for whether bidiagonal matrix is low(:L) bidiagonal or up(:U) bidiagonal. · Issue #33402 · JuliaLang/julia · GitHub is another case where banded matrices could/should be used in Base as the output type of an operation to allow for further optimizations, but currently the output is just a pure sparse matrix. @dlfivefifty mentioned in Check bands for zeros in `lu!` and `qr!` · Issue #197 · JuliaLinearAlgebra/BandedMatrices.jl · GitHub that it can’t be added to the StdLib yet because of ArrayLayouts.jl, but I think there’s more than a few cases where Base should be using BandedMatrix types in some places and so the only way to get the efficient algorithm would be to have some form of a BandedMatrix in Base, or to just copy some of the methods over and have the best possible algorithm in Base.
Banded matrices just show up as such a common form that I think we’re losing out by not having them in our pool of go-to things that Base is allowed to give you and specialize on.