Restrict to real/complex numbers

Author: jishnub

src/adjtrans.jl

@@ -513,8 +513,9 @@ function _dot_nonrecursive(u, v)
     end
 end
 
-rmul!(X::AdjOrTrans, s::Number) = (lmul!(wrapperop(X)(s), parent(X)); X)
-lmul!(s::Number, X::AdjOrTrans) = (rmul!(parent(X), wrapperop(X)(s)); X)
+# we use (n A^T) = (A n)^T, which holds if the product of n and the elements of A is commutative
+rmul!(X::AdjOrTrans{<:Union{Real,Complex}}, s::Union{Real,Complex}) = (lmul!(wrapperop(X)(s), parent(X)); X)
+lmul!(s::Union{Real,Complex}, X::AdjOrTrans{<:Union{Real,Complex}}) = (rmul!(parent(X), wrapperop(X)(s)); X)
 
 # Adjoint/Transpose-vector * vector
 *(u::AdjointAbsVec{<:Number}, v::AbstractVector{<:Number}) = dot(u.parent, v)

test/adjtrans.jl

@@ -12,6 +12,7 @@ isdefined(Main, :LinearAlgebraTestHelpers) || Base.include(Main, TESTHELPERS)
 
 using Main.LinearAlgebraTestHelpers.OffsetArrays
 using Main.LinearAlgebraTestHelpers.ImmutableArrays
+using Main.LinearAlgebraTestHelpers.Quaternions
 
 @testset "Adjoint and Transpose inner constructor basics" begin
     intvec, intmat = [1, 2], [1 2; 3 4]
@@ -811,7 +812,8 @@ end
 
 @testset "lmul!/rmul! by numbers" begin
     @testset "$(eltype(A))" for A in (rand(4, 4), rand(ComplexF64,4,4),
-                fill([1 2; 3 4], 4, 4))
+                fill([1 2; 3 4], 4, 4),
+                fill(Quaternion(1,2,3,4), 4, 4))
         B = copy(A)
         @testset for op in (transpose, adjoint)
             A .= B
@@ -824,6 +826,13 @@ end
                 A .= B
                 @test rmul!(op(A), -2im) == op(B) * -2im
             end
+            if eltype(A) <: Quaternion
+                A .= B
+                q = Quaternion(0,1,4,7)
+                @test lmul!(q, op(A)) == q * op(B)
+                A .= B
+                @test rmul!(op(A), q) == op(B) * q
+            end
         end
     end
 end