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Clarify the role of pivoting in QR factorization #29976

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Clarify the role of pivoting in QR factorization
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mzaffalon authored Nov 9, 2018
commit 453634999152a049cf4e86997a6feeb54c01fefc
4 changes: 3 additions & 1 deletion stdlib/LinearAlgebra/src/qr.jl
Original file line number Diff line number Diff line change
@@ -318,7 +318,9 @@ Iterating the decomposition produces the components `Q`, `R`, and if extant `p`.

The following functions are available for the `QR` objects: [`inv`](@ref), [`size`](@ref),
and [`\\`](@ref). When `A` is rectangular, `\\` will return a least squares
solution and if the solution is not unique, the one with smallest norm is returned.
solution and if the solution is not unique, the one with smallest norm is returned. When
`A` is not full rank, factorization with (column) pivoting is required to obtain a finite
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I'm not sure about the "finite norm solution" part here. I'd expect it to be a "unique solution" or "minimum norm solution".

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You are right. After I submitted it, I also thought it was badly formulated. I will change it when I get home.

norm solution.

Multiplication with respect to either full/square or non-full/square `Q` is allowed, i.e. both `F.Q*F.R`
and `F.Q*A` are supported. A `Q` matrix can be converted into a regular matrix with