diff --git a/stdlib/LinearAlgebra/src/generic.jl b/stdlib/LinearAlgebra/src/generic.jl
index bdd11dc822ef3..f60016125d2e9 100644
--- a/stdlib/LinearAlgebra/src/generic.jl
+++ b/stdlib/LinearAlgebra/src/generic.jl
@@ -1676,7 +1676,7 @@ 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)