From 0429e1edd5e085fa2eb997f6e08504efd9aa7db2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mateus=20Ara=C3=BAjo?= <maltusan@gmail.com>
Date: Thu, 25 Jul 2024 10:02:50 +0200
Subject: [PATCH] [docs] change docstring to match code (#55013)
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The docstring of `LinearAlgebra.reflectorApply!` is incorrect. It says
the function is applying `(I - τ*[1; x] * [1; x]')*A`, but in reality it
is applying `(I - conj(τ)*[1; x[2:end]]*[1; x[2:end]]')*A`. You can
check that by looking at the code, or running for example
```julia
using LinearAlgebra
T=ComplexF64;d=5;
τ=randn(T);x=randn(T,d);A=randn(T,d,d);
(I - conj(τ)*[1; x[2:end]]*[1; x[2:end]]')*A
LinearAlgebra.reflectorApply!(x,τ,A)
```

(cherry picked from commit 1ece299e4a1ebf9410099d2442c8dd2a19f9f615)
---
 stdlib/LinearAlgebra/src/generic.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stdlib/LinearAlgebra/src/generic.jl b/stdlib/LinearAlgebra/src/generic.jl
index c2144bf85d024..295f91878ee74 100644
--- a/stdlib/LinearAlgebra/src/generic.jl
+++ b/stdlib/LinearAlgebra/src/generic.jl
@@ -1607,7 +1607,7 @@ end
 """
     reflectorApply!(x, τ, A)
 
-Multiplies `A` in-place by a Householder reflection on the left. It is equivalent to `A .= (I - τ*[1; x] * [1; x]')*A`.
+Multiplies `A` in-place by a Householder reflection on the left. It is equivalent to `A .= (I - conj(τ)*[1; x[2:end]]*[1; x[2:end]]')*A`.
 """
 @inline function reflectorApply!(x::AbstractVector, τ::Number, A::AbstractVecOrMat)
     require_one_based_indexing(x)