From 4e767a3a78d93f88ca95a30429113fa63d83bd09 Mon Sep 17 00:00:00 2001 From: Michele Zaffalon Date: Wed, 21 Nov 2018 16:43:59 +0100 Subject: [PATCH] Clarify the role of pivoting in QR factorization (#29976) * Clarify the role of pivoting in QR factorization Ref: https://discourse.julialang.org/t/left-matrix-division-with-singular-matrix/15503 * Update qr.jl (cherry picked from commit e5e6b6438757691d186440a23c594f744125c859) --- stdlib/LinearAlgebra/src/qr.jl | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/stdlib/LinearAlgebra/src/qr.jl b/stdlib/LinearAlgebra/src/qr.jl index d3646af06ac928..7607bce96db270 100644 --- a/stdlib/LinearAlgebra/src/qr.jl +++ b/stdlib/LinearAlgebra/src/qr.jl @@ -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 minimum +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