diff --git a/src/Arpack.jl b/src/Arpack.jl
index ebc3f3a..674428e 100644
--- a/src/Arpack.jl
+++ b/src/Arpack.jl
@@ -222,10 +222,10 @@ struct AtA_or_AAt{T,S} <: AbstractArray{T, 2}
     buffer::Vector{T}
 end
 
-function AtA_or_AAt(A::AbstractMatrix{T}) where T
+function AtA_or_AAt(A)
+    T    = eltype(A)
     Tnew = typeof(zero(T)/sqrt(one(T)))
-    Anew = convert(AbstractMatrix{Tnew}, A)
-    AtA_or_AAt{Tnew,typeof(Anew)}(Anew, Vector{Tnew}(undef, max(size(A)...)))
+    return AtA_or_AAt{Tnew,typeof(A)}(A, Vector{Tnew}(undef, max(size(A)...)))
 end
 
 function LinearAlgebra.mul!(y::StridedVector{T}, A::AtA_or_AAt{T}, x::StridedVector{T}) where T
diff --git a/test/runtests.jl b/test/runtests.jl
index 4f43a68..0797101 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -281,3 +281,17 @@ end
     @test_throws MethodError eigs(big.(rand(1:10, 10, 10)), rand(1:10, 10, 10))
     @test_throws MethodError svds(big.(rand(1:10, 10, 8)))
 end
+
+struct MyOp{S}
+    mat::S
+end
+Base.size(A::MyOp) = size(A.mat)
+Base.size(A::MyOp, i::Integer) = size(A.mat, i)
+Base.eltype(A::MyOp) = Float64
+Base.:*(A::MyOp, B::AbstractMatrix) = A.mat*B
+LinearAlgebra.mul!(y::AbstractVector, A::MyOp, x::AbstractVector) = mul!(y, A.mat, x)
+LinearAlgebra.adjoint(A::MyOp) = MyOp(adjoint(A.mat))
+@testset "svds for non-AbstractMatrix" begin
+    A = MyOp(randn(10, 9))
+    @test svds(A, v0 = ones(9))[1].S == svds(A.mat, v0 = ones(9))[1].S
+end