diff --git a/Project.toml b/Project.toml
index a0d0237..991b367 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "PDMats"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.11.10"
+version = "0.11.11"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/README.md b/README.md
index 8d35702..407e7a2 100644
--- a/README.md
+++ b/README.md
@@ -209,6 +209,18 @@ unwhiten!(a, x)     # un-whitening transform inplace, updating `x`.
 unwhiten!(r, a, x)  # write the transformed result to `r`.
 ```
 
+### Fallbacks for `AbstractArray`s
+For ease of composability, some of these functions have generic fallbacks defined that work on `AbstractArray`s.
+These fallbacks may not be as fast as the methods specializaed for `AbstractPDMat`s, but they let you more easily swap out types.
+While in theory all of them can be defined, at present only the following subset has:
+
+ - `dim`
+ - `whiten`, `whiten!`
+ - `unwhiten`, `unwhiten!`
+ - `quad`, `quad!`
+ - `invquad`, `invquad!`
+
+PRs to implement more generic fallbacks are welcome.
 
 ## Define Customized Subtypes
 
diff --git a/src/generics.jl b/src/generics.jl
index 14828c3..2742a18 100644
--- a/src/generics.jl
+++ b/src/generics.jl
@@ -1,11 +1,15 @@
 # Generic functions (on top of the type-specific implementations)
 
 ## Basic functions
-
 Base.size(a::AbstractPDMat) = (dim(a), dim(a))
 Base.size(a::AbstractPDMat, i::Integer) = 1 <= i <= 2 ? dim(a) : 1
 Base.length(a::AbstractPDMat) = abs2(dim(a))
 
+function dim(a::AbstractMatrix)
+    @check_argdims size(a, 1) == size(a, 2)
+    return size(a, 1)
+end
+
 ## arithmetics
 
 pdadd!(r::Matrix, a::Matrix, b::AbstractPDMat{T}) where {T<:Real} = pdadd!(r, a, b, one(T))
@@ -29,16 +33,25 @@ LinearAlgebra.isposdef(::AbstractPDMat) = true
 LinearAlgebra.ishermitian(::AbstractPDMat) = true
 
 ## whiten and unwhiten
-whiten!(a::AbstractPDMat, x::StridedVecOrMat) = whiten!(x, a, x)
-unwhiten!(a::AbstractPDMat, x::StridedVecOrMat) = unwhiten!(x, a, x)
+
+whiten!(a::AbstractMatrix, x::AbstractVecOrMat) = whiten!(x, a, x)
+unwhiten!(a::AbstractMatrix, x::AbstractVecOrMat) = unwhiten!(x, a, x)
+
+function whiten!(r::AbstractVecOrMat, a::AbstractMatrix, x::AbstractVecOrMat)
+    v = _rcopy!(r, x)
+    ldiv!(chol_lower(cholesky(a)), v)
+end
+
+function unwhiten!(r::AbstractVecOrMat, a::AbstractMatrix, x::AbstractVecOrMat)
+    v = _rcopy!(r, x)
+    lmul!(chol_lower(cholesky(a)), v)
+end
 
 """
-    whiten(a::AbstractPDMat, x::StridedVecOrMat)
-    whiten!(a::AbstractPDMat, x::StridedVecOrMat)
-    whiten!(r::StridedVecOrMat, a::AbstractPDMat, x::StridedVecOrMat)
-    unwhiten(a::AbstractPDMat, x::StridedVecOrMat)
-    unwhiten!(a::AbstractPDMat, x::StridedVecOrMat)
-    unwhiten!(r::StridedVecOrMat, a::AbstractPDMat, x::StridedVecOrMat)
+    whiten(a::AbstractMatrix, x::AbstractVecOrMat)
+    unwhiten(a::AbstractMatrix, x::AbstractVecOrMat)
+    unwhiten!(a::AbstractMatrix, x::AbstractVecOrMat)
+    unwhiten!(r::AbstractVecOrMat, a::AbstractPDMat, x::AbstractVecOrMat)
 
 Allocating and in-place versions of the `whiten`ing transform (or its inverse) defined by `a` applied to `x`
 
@@ -68,28 +81,38 @@ julia> W * W'
  0.0  1.0
 ```
 """
-whiten(a::AbstractPDMat, x::StridedVecOrMat) = whiten!(similar(x), a, x)
-unwhiten(a::AbstractPDMat, x::StridedVecOrMat) = unwhiten!(similar(x), a, x)
+whiten(a::AbstractMatrix, x::AbstractVecOrMat) = whiten!(similar(x), a, x)
+unwhiten(a::AbstractMatrix, x::AbstractVecOrMat) = unwhiten!(similar(x), a, x)
 
 
 ## quad
 
 """
-    quad(a::AbstractPDMat, x::StridedVecOrMat)
+    quad(a::AbstractMatrix, x::AbstractVecOrMat)
 
 Return the value of the quadratic form defined by `a` applied to `x`
 
 If `x` is a vector the quadratic form is `x' * a * x`.  If `x` is a matrix
 the quadratic form is applied column-wise.
 """
-function quad(a::AbstractPDMat{T}, x::StridedMatrix{S}) where {T<:Real, S<:Real}
+function quad(a::AbstractMatrix{T}, x::AbstractMatrix{S}) where {T<:Real, S<:Real}
     @check_argdims dim(a) == size(x, 1)
     quad!(Array{promote_type(T, S)}(undef, size(x,2)), a, x)
 end
 
+quad(a::AbstractMatrix, x::AbstractVector) = sum(abs2, chol_upper(cholesky(a)) * x)
+invquad(a::AbstractMatrix, x::AbstractVector) = sum(abs2, chol_lower(cholesky(a)) \ x)
 
 """
-    invquad(a::AbstractPDMat, x::StridedVecOrMat)
+    quad!(r::AbstractArray, a::AbstractMatrix, x::AbstractMatrix)
+
+Overwrite `r` with the value of the quadratic form defined by `a` applied columnwise to `x`
+"""
+quad!(r::AbstractArray, a::AbstractMatrix, x::AbstractMatrix) = colwise_dot!(r, x, a * x)
+
+
+"""
+    invquad(a::AbstractMatrix, x::AbstractVecOrMat)
 
 Return the value of the quadratic form defined by `inv(a)` applied to `x`.
 
@@ -98,7 +121,15 @@ For most `PDMat` types this is done in a way that does not require evaluation of
 If `x` is a vector the quadratic form is `x' * a * x`.  If `x` is a matrix
 the quadratic form is applied column-wise.
 """
-function invquad(a::AbstractPDMat{T}, x::StridedMatrix{S}) where {T<:Real, S<:Real}
+invquad(a::AbstractMatrix, x::AbstractVecOrMat) = x' / a * x
+function invquad(a::AbstractMatrix{T}, x::AbstractMatrix{S}) where {T<:Real, S<:Real}
     @check_argdims dim(a) == size(x, 1)
     invquad!(Array{promote_type(T, S)}(undef, size(x,2)), a, x)
 end
+
+"""
+    invquad!(r::AbstractArray, a::AbstractMatrix, x::AbstractMatrix)
+
+Overwrite `r` with the value of the quadratic form defined by `inv(a)` applied columnwise to `x`
+"""
+invquad!(r::AbstractArray, a::AbstractMatrix, x::AbstractMatrix) = colwise_dot!(r, x, a \ x)
diff --git a/src/pdmat.jl b/src/pdmat.jl
index 5afbd83..ab613f7 100644
--- a/src/pdmat.jl
+++ b/src/pdmat.jl
@@ -60,39 +60,6 @@ LinearAlgebra.eigmin(a::PDMat) = eigmin(a.mat)
 Base.kron(A::PDMat, B::PDMat) = PDMat(kron(A.mat, B.mat), Cholesky(kron(A.chol.U, B.chol.U), 'U', A.chol.info))
 LinearAlgebra.sqrt(A::PDMat) = PDMat(sqrt(Hermitian(A.mat)))
 
-### whiten and unwhiten
-
-function whiten!(r::StridedVecOrMat, a::PDMat, x::StridedVecOrMat)
-    v = _rcopy!(r, x)
-    ldiv!(chol_lower(a.chol), v)
-end
-
-function unwhiten!(r::StridedVecOrMat, a::PDMat, x::StridedVecOrMat)
-    v = _rcopy!(r, x)
-    lmul!(chol_lower(a.chol), v)
-end
-
-
-### quadratic forms
-
-quad(a::PDMat, x::AbstractVector) = sum(abs2, chol_upper(a.chol) * x)
-invquad(a::PDMat, x::AbstractVector) = sum(abs2, chol_lower(a.chol) \ x)
-
-"""
-    quad!(r::AbstractArray, a::AbstractPDMat, x::StridedMatrix)
-
-Overwrite `r` with the value of the quadratic form defined by `a` applied columnwise to `x`
-"""
-quad!(r::AbstractArray, a::PDMat, x::StridedMatrix) = colwise_dot!(r, x, a.mat * x)
-
-"""
-    invquad!(r::AbstractArray, a::AbstractPDMat, x::StridedMatrix)
-
-Overwrite `r` with the value of the quadratic form defined by `inv(a)` applied columnwise to `x`
-"""
-invquad!(r::AbstractArray, a::PDMat, x::StridedMatrix) = colwise_dot!(r, x, a.mat \ x)
-
-
 ### tri products
 
 function X_A_Xt(a::PDMat, x::AbstractMatrix)
diff --git a/src/utils.jl b/src/utils.jl
index 6385218..708440e 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -7,7 +7,7 @@ macro check_argdims(cond)
     end
 end
 
-_rcopy!(r::StridedVecOrMat, x::StridedVecOrMat) = (r === x || copyto!(r, x); r)
+_rcopy!(r, x) = (r === x || copyto!(r, x); r)
 
 
 function _addscal!(r::Matrix, a::Matrix, b::Union{Matrix, SparseMatrixCSC}, c::Real)
@@ -69,11 +69,11 @@ function invwsumsq(w::AbstractVector, a::AbstractVector)
 end
 
 function colwise_dot!(r::AbstractArray, a::AbstractMatrix, b::AbstractMatrix)
-    n = length(r)
-    @check_argdims n == size(a, 2) == size(b, 2) && size(a, 1) == size(b, 1)
-    for j = 1:n
+    @check_argdims(axes(a) == axes(b))
+    @check_argdims(axes(a, 2) == eachindex(r))
+    for j in axes(a, 2)
         v = zero(promote_type(eltype(a), eltype(b)))
-        @simd for i = 1:size(a, 1)
+        @simd for i in axes(a, 1)
             @inbounds v += a[i, j]*b[i, j]
         end
         r[j] = v
diff --git a/test/abstracttypes.jl b/test/abstracttypes.jl
new file mode 100644
index 0000000..fa1de42
--- /dev/null
+++ b/test/abstracttypes.jl
@@ -0,0 +1,23 @@
+using Test, PDMats
+
+@testset "AbstractMatrix fallback functionality" begin
+    C = Cmat = [4. -2. -1.; -2. 5. -1.; -1. -1. 6.]
+    
+    test_pdmat(C, Cmat;
+        verbose=2,             # the level to display intermediate steps
+        cmat_eq=true,          # require Cmat and Matrix(C) to be exactly equal
+        t_diag=false,          # whether to test diag method
+        t_cholesky=false,      # whether to test cholesky method
+        t_scale=false,         # whether to test scaling
+        t_add=false,           # whether to test pdadd
+        t_det=false,           # whether to test det method
+        t_logdet=false,        # whether to test logdet method
+        t_eig=false,           # whether to test eigmax and eigmin
+        t_mul=false,           # whether to test multiplication
+        t_div=false,           # whether to test division
+        t_quad=true,           # whether to test quad & invquad
+        t_triprod=false,       # whether to test X_A_Xt, Xt_A_X, X_invA_Xt, and Xt_invA_X
+        t_whiten=true          # whether to test whiten and unwhiten
+    )
+
+end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 1a99ffa..293fec2 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,5 +1,5 @@
 include("testutils.jl")
-tests = ["pdmtypes", "addition", "generics", "kron", "chol", "specialarrays", "sqrt"]
+tests = ["pdmtypes", "abstracttypes", "addition", "generics", "kron", "chol", "specialarrays", "sqrt"]
 println("Running tests ...")
 
 for t in tests
diff --git a/test/testutils.jl b/test/testutils.jl
index 38eff6d..75e179e 100644
--- a/test/testutils.jl
+++ b/test/testutils.jl
@@ -10,7 +10,7 @@ const HAVE_CHOLMOD = isdefined(SuiteSparse, :CHOLMOD)
 const PDMatType = HAVE_CHOLMOD ? Union{PDMat, PDSparseMat, PDiagMat} : Union{PDMat, PDiagMat}
 
 ## driver function
-function test_pdmat(C::AbstractPDMat, Cmat::Matrix;
+function test_pdmat(C, Cmat::Matrix;
                     verbose::Int=2,             # the level to display intermediate steps
                     cmat_eq::Bool=false,        # require Cmat and Matrix(C) to be exactly equal
                     t_diag::Bool=true,          # whether to test diag method
@@ -62,7 +62,7 @@ end
 _pdt(vb::Int, s) = (vb >= 2 && printstyled("    .. testing $s\n", color=:green))
 
 
-function pdtest_basics(C::AbstractPDMat, Cmat::Matrix, d::Int, verbose::Int)
+function pdtest_basics(C, Cmat::Matrix, d::Int, verbose::Int)
     _pdt(verbose, "dim")
     @test dim(C) == d
 
@@ -94,7 +94,7 @@ function pdtest_basics(C::AbstractPDMat, Cmat::Matrix, d::Int, verbose::Int)
 end
 
 
-function pdtest_cmat(C::AbstractPDMat, Cmat::Matrix, cmat_eq::Bool, verbose::Int)
+function pdtest_cmat(C, Cmat::Matrix, cmat_eq::Bool, verbose::Int)
     _pdt(verbose, "full")
     if cmat_eq
         @test Matrix(C) == Cmat
@@ -104,7 +104,7 @@ function pdtest_cmat(C::AbstractPDMat, Cmat::Matrix, cmat_eq::Bool, verbose::Int
 end
 
 
-function pdtest_diag(C::AbstractPDMat, Cmat::Matrix, cmat_eq::Bool, verbose::Int)
+function pdtest_diag(C, Cmat::Matrix, cmat_eq::Bool, verbose::Int)
     _pdt(verbose, "diag")
     if cmat_eq
         @test diag(C) == diag(Cmat)
@@ -133,14 +133,14 @@ if HAVE_CHOLMOD
     end
 end
 
-function pdtest_scale(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
+function pdtest_scale(C, Cmat::Matrix, verbose::Int)
     _pdt(verbose, "scale")
     @test Matrix(C * convert(eltype(C),2)) ≈ Cmat * convert(eltype(C),2)
     @test Matrix(convert(eltype(C),2) * C) ≈ convert(eltype(C),2) * Cmat
 end
 
 
-function pdtest_add(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
+function pdtest_add(C, Cmat::Matrix, verbose::Int)
     M = rand(eltype(C),size(Cmat))
     _pdt(verbose, "add")
     @test C + M ≈ Cmat + M
@@ -156,7 +156,7 @@ function pdtest_add(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
     @test Mr ≈ R
 end
 
-function pdtest_det(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
+function pdtest_det(C, Cmat::Matrix, verbose::Int)
     _pdt(verbose, "det")
     @test det(C) ≈ det(Cmat)
 
@@ -166,7 +166,7 @@ function pdtest_det(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
     end
 end
 
-function pdtest_logdet(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
+function pdtest_logdet(C, Cmat::Matrix, verbose::Int)
     _pdt(verbose, "logdet")
     @test logdet(C) ≈ logdet(Cmat)
 
@@ -177,7 +177,7 @@ function pdtest_logdet(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
 end
 
 
-function pdtest_eig(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
+function pdtest_eig(C, Cmat::Matrix, verbose::Int)
     _pdt(verbose, "eigmax")
     @test eigmax(C) ≈ eigmax(Cmat)
 
@@ -186,14 +186,14 @@ function pdtest_eig(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
 end
 
 
-function pdtest_mul(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
+function pdtest_mul(C, Cmat::Matrix, verbose::Int)
     n = 5
     X = rand(eltype(C), dim(C), n)
     pdtest_mul(C, Cmat, X, verbose)
 end
 
 
-function pdtest_mul(C::AbstractPDMat, Cmat::Matrix, X::Matrix, verbose::Int)
+function pdtest_mul(C, Cmat::Matrix, X::Matrix, verbose::Int)
     _pdt(verbose, "multiply")
     d, n = size(X)
     @assert d == dim(C)
@@ -217,7 +217,7 @@ function pdtest_mul(C::AbstractPDMat, Cmat::Matrix, X::Matrix, verbose::Int)
 end
 
 
-function pdtest_div(C::AbstractPDMat, Imat::Matrix, X::Matrix, verbose::Int)
+function pdtest_div(C, Imat::Matrix, X::Matrix, verbose::Int)
     _pdt(verbose, "divide")
     d, n = size(X)
     @assert d == dim(C)
@@ -246,7 +246,7 @@ function pdtest_div(C::AbstractPDMat, Imat::Matrix, X::Matrix, verbose::Int)
 end
 
 
-function pdtest_quad(C::AbstractPDMat, Cmat::Matrix, Imat::Matrix, X::Matrix, verbose::Int)
+function pdtest_quad(C, Cmat::Matrix, Imat::Matrix, X::Matrix, verbose::Int)
     n = size(X, 2)
 
     _pdt(verbose, "quad")
@@ -271,7 +271,7 @@ function pdtest_quad(C::AbstractPDMat, Cmat::Matrix, Imat::Matrix, X::Matrix, ve
 end
 
 
-function pdtest_triprod(C::AbstractPDMat, Cmat::Matrix, Imat::Matrix, X::Matrix, verbose::Int)
+function pdtest_triprod(C, Cmat::Matrix, Imat::Matrix, X::Matrix, verbose::Int)
     d, n = size(X)
     @assert d == dim(C)
     Xt = copy(transpose(X))
@@ -298,7 +298,7 @@ function pdtest_triprod(C::AbstractPDMat, Cmat::Matrix, Imat::Matrix, X::Matrix,
 end
 
 
-function pdtest_whiten(C::AbstractPDMat, Cmat::Matrix, verbose::Int)
+function pdtest_whiten(C, Cmat::Matrix, verbose::Int)
     Y = PDMats.chol_lower(Cmat)
     Q = qr(convert(Array{eltype(C),2},randn(size(Cmat)))).Q
     Y = Y * Q'                    # generate a matrix Y such that Y * Y' = C