From a6fe51a6692e32a3525dd78b30718082e4ab4fab Mon Sep 17 00:00:00 2001
From: Sheehan Olver <solver@mac.com>
Date: Mon, 11 May 2020 11:31:08 +0100
Subject: [PATCH] Add `inv(::AbstractQ)` (#35826)

* Override `inv` for `AbstractQ`

* Add test for inv

* Update qr.jl

Co-authored-by: Andreas Noack <andreas@noack.dk>
---
 stdlib/LinearAlgebra/src/qr.jl  | 2 ++
 stdlib/LinearAlgebra/test/qr.jl | 7 +++++++
 2 files changed, 9 insertions(+)

diff --git a/stdlib/LinearAlgebra/src/qr.jl b/stdlib/LinearAlgebra/src/qr.jl
index 995aa1ce8c895f..d60fc2458dea3c 100644
--- a/stdlib/LinearAlgebra/src/qr.jl
+++ b/stdlib/LinearAlgebra/src/qr.jl
@@ -467,6 +467,8 @@ Base.propertynames(F::QRPivoted, private::Bool=false) =
 
 abstract type AbstractQ{T} <: AbstractMatrix{T} end
 
+inv(Q::AbstractQ) = Q'
+
 """
     QRPackedQ <: AbstractMatrix
 
diff --git a/stdlib/LinearAlgebra/test/qr.jl b/stdlib/LinearAlgebra/test/qr.jl
index 3d6247798067ea..f1d24a06a45bf9 100644
--- a/stdlib/LinearAlgebra/test/qr.jl
+++ b/stdlib/LinearAlgebra/test/qr.jl
@@ -297,4 +297,11 @@ end
     end
 end
 
+@testset "inv(::AbstractQ)" begin
+    for T in (Float64, ComplexF64)
+        Q = qr(randn(T,5,5)).Q
+        @test inv(Q) === Q'
+    end
+end
+
 end # module TestQR