diff --git a/Project.toml b/Project.toml
index c40adca6c..ba9907272 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "LinearSolve"
 uuid = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 authors = ["SciML"]
-version = "2.21.0"
+version = "2.21.1"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
diff --git a/src/default.jl b/src/default.jl
index 4c4b43a1f..0d2daf19c 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -101,7 +101,7 @@ end
     end
 end
 
-function defaultalg(A::GPUArraysCore.AbstractGPUArray, b, assump::OperatorAssumptions{Bool})
+function defaultalg(A::GPUArraysCore.AnyGPUArray, b, assump::OperatorAssumptions{Bool})
     if assump.condition === OperatorCondition.IllConditioned || !assump.issq
         DefaultLinearSolver(DefaultAlgorithmChoice.QRFactorization)
     else
@@ -110,7 +110,7 @@ function defaultalg(A::GPUArraysCore.AbstractGPUArray, b, assump::OperatorAssump
 end
 
 # A === nothing case
-function defaultalg(A::Nothing, b::GPUArraysCore.AbstractGPUArray, assump::OperatorAssumptions{Bool})
+function defaultalg(A::Nothing, b::GPUArraysCore.AnyGPUArray, assump::OperatorAssumptions{Bool})
     if assump.condition === OperatorCondition.IllConditioned || !assump.issq
         DefaultLinearSolver(DefaultAlgorithmChoice.QRFactorization)
     else
@@ -119,7 +119,7 @@ function defaultalg(A::Nothing, b::GPUArraysCore.AbstractGPUArray, assump::Opera
 end
 
 # Ambiguity handling
-function defaultalg(A::GPUArraysCore.AbstractGPUArray, b::GPUArraysCore.AbstractGPUArray,
+function defaultalg(A::GPUArraysCore.AnyGPUArray, b::GPUArraysCore.AbstractGPUArray,
     assump::OperatorAssumptions{Bool})
     if assump.condition === OperatorCondition.IllConditioned || !assump.issq
         DefaultLinearSolver(DefaultAlgorithmChoice.QRFactorization)
diff --git a/src/factorization.jl b/src/factorization.jl
index 59ade8266..cb0c2b2e6 100644
--- a/src/factorization.jl
+++ b/src/factorization.jl
@@ -78,6 +78,8 @@ function do_factorization(alg::LUFactorization, A, b, u)
     if A isa AbstractSparseMatrixCSC
         return lu(SparseMatrixCSC(size(A)..., getcolptr(A), rowvals(A), nonzeros(A)),
             check = false)
+    elseif A isa GPUArraysCore.AnyGPUArray
+        fact = lu(A; check = false)
     elseif !ArrayInterface.can_setindex(typeof(A))
         fact = lu(A, alg.pivot, check = false)
     else
@@ -98,6 +100,16 @@ function init_cacheval(alg::Union{LUFactorization, GenericLUFactorization}, A, b
     ArrayInterface.lu_instance(convert(AbstractMatrix, A))
 end
 
+function init_cacheval(alg::Union{LUFactorization, GenericLUFactorization},
+    A::Union{<:Adjoint, <:Transpose}, b, u, Pl, Pr, maxiters::Int, abstol, reltol,
+    verbose::Bool, assumptions::OperatorAssumptions)
+    if alg isa LUFactorization
+        return lu(A; check=false)
+    else
+        return LinearAlgebra.generic_lufact!(copy(A), alg.pivot; check=false)
+    end
+end
+
 const PREALLOCATED_LU = ArrayInterface.lu_instance(rand(1, 1))
 
 function init_cacheval(alg::Union{LUFactorization, GenericLUFactorization},
@@ -143,7 +155,7 @@ end
 function do_factorization(alg::QRFactorization, A, b, u)
     A = convert(AbstractMatrix, A)
     if ArrayInterface.can_setindex(typeof(A))
-        if alg.inplace && !(A isa SparseMatrixCSC) && !(A isa GPUArraysCore.AbstractGPUArray)
+        if alg.inplace && !(A isa SparseMatrixCSC) && !(A isa GPUArraysCore.AnyGPUArray)
             fact = qr!(A, alg.pivot)
         else
             fact = qr(A) # CUDA.jl does not allow other args!
@@ -160,6 +172,12 @@ function init_cacheval(alg::QRFactorization, A, b, u, Pl, Pr,
     ArrayInterface.qr_instance(convert(AbstractMatrix, A), alg.pivot)
 end
 
+function init_cacheval(alg::QRFactorization, A::Union{<:Adjoint, <:Transpose}, b, u, Pl, Pr,
+    maxiters::Int, abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
+    A isa GPUArraysCore.AnyGPUArray && return qr(A)
+    return qr(A, alg.pivot)
+end
+
 const PREALLOCATED_QR = ArrayInterface.qr_instance(rand(1, 1))
 
 function init_cacheval(alg::QRFactorization{NoPivot}, A::Matrix{Float64}, b, u, Pl, Pr,
@@ -204,6 +222,8 @@ function do_factorization(alg::CholeskyFactorization, A, b, u)
     A = convert(AbstractMatrix, A)
     if A isa SparseMatrixCSC
         fact = cholesky(A; shift = alg.shift, check = false, perm = alg.perm)
+    elseif A isa GPUArraysCore.AnyGPUArray
+        fact = cholesky(A; check = false)
     elseif alg.pivot === Val(false) || alg.pivot === NoPivot()
         fact = cholesky!(A, alg.pivot; check = false)
     else
@@ -218,9 +238,13 @@ function init_cacheval(alg::CholeskyFactorization, A::SMatrix{S1, S2}, b, u, Pl,
     cholesky(A)
 end
 
+function init_cacheval(alg::CholeskyFactorization, A::GPUArraysCore.AnyGPUArray, b, u, Pl,
+    Pr, maxiters::Int, abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
+    cholesky(A; check=false)
+end
+
 function init_cacheval(alg::CholeskyFactorization, A, b, u, Pl, Pr,
-    maxiters::Int, abstol, reltol, verbose::Bool,
-    assumptions::OperatorAssumptions)
+    maxiters::Int, abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
     ArrayInterface.cholesky_instance(convert(AbstractMatrix, A), alg.pivot)
 end
 
@@ -968,7 +992,7 @@ default_alias_b(::NormalCholeskyFactorization, ::Any, ::Any) = true
 const PREALLOCATED_NORMALCHOLESKY = ArrayInterface.cholesky_instance(rand(1, 1), NoPivot())
 
 function init_cacheval(alg::NormalCholeskyFactorization,
-    A::Union{AbstractSparseArray, GPUArraysCore.AbstractGPUArray,
+    A::Union{AbstractSparseArray, GPUArraysCore.AnyGPUArray,
         Symmetric{<:Number, <:AbstractSparseArray}}, b, u, Pl, Pr,
     maxiters::Int, abstol, reltol, verbose::Bool,
     assumptions::OperatorAssumptions)
@@ -999,7 +1023,7 @@ function SciMLBase.solve!(cache::LinearCache, alg::NormalCholeskyFactorization;
     A = cache.A
     A = convert(AbstractMatrix, A)
     if cache.isfresh
-        if A isa SparseMatrixCSC || A isa GPUArraysCore.AbstractGPUArray || A isa SMatrix
+        if A isa SparseMatrixCSC || A isa GPUArraysCore.AnyGPUArray || A isa SMatrix
             fact = cholesky(Symmetric((A)' * A); check = false)
         else
             fact = cholesky(Symmetric((A)' * A), alg.pivot; check = false)
diff --git a/test/gpu/cuda.jl b/test/gpu/cuda.jl
index 75a181026..5e0e5518e 100644
--- a/test/gpu/cuda.jl
+++ b/test/gpu/cuda.jl
@@ -73,3 +73,19 @@ using BlockDiagonals
 
     @test solve(prob1, SimpleGMRES(; blocksize = 2)).u ≈ solve(prob2, SimpleGMRES()).u
 end
+
+# Test Dispatches for Adjoint/Transpose Types
+A = Matrix(Hermitian(rand(5, 5) + I)) |> cu
+b = rand(5) |> cu
+prob1 = LinearProblem(A', b)
+prob2 = LinearProblem(transpose(A), b)
+
+@testset "Adjoint/Transpose Type: $(alg)" for alg in (NormalCholeskyFactorization(),
+        CholeskyFactorization(), LUFactorization(), QRFactorization(), nothing)
+    sol = solve(prob1, alg; alias_A = false)
+    @test norm(A' * sol.u .- b) < 1e-5
+    @show sol.u, A' \ b
+
+    sol = solve(prob2, alg; alias_A = false)
+    @test norm(transpose(A) * sol.u .- b) < 1e-5
+end