diff --git a/stdlib/LinearAlgebra/src/symmetriceigen.jl b/stdlib/LinearAlgebra/src/symmetriceigen.jl
index 08c8c61c5d354d..7694036ca5f2b9 100644
--- a/stdlib/LinearAlgebra/src/symmetriceigen.jl
+++ b/stdlib/LinearAlgebra/src/symmetriceigen.jl
@@ -196,7 +196,8 @@ function eigvals!(A::Hermitian{T,S}, B::Hermitian{T,S}; sortby::Union{Function,N
 end
 eigvecs(A::HermOrSym) = eigvecs(eigen(A))
 
-# For A::StridedMatrix and B::Hermitian, a call to LAPACK is faster. See: https://github.com/JuliaLang/julia/issues/49533
+# For A::StridedMatrix and B::Hermitian, a call to LAPACK is faster. However, for matrix sizes beyond 1000x1000 and 
+# positive semidefinite matrices, a Cholesky decomposition based approach may be better, see See: https://github.com/JuliaLang/julia/issues/49533
 function eigvals!(A::StridedMatrix{T}, B::HermOrSym{T,S}; sortby::Union{Function,Nothing}=nothing) where {T<:BlasReal,S<:StridedMatrix}
     return eigvals!(A, Matrix{T}(B); sortby)
 end