diff --git a/Project.toml b/Project.toml
index da7b104..dfd57c7 100644
--- a/Project.toml
+++ b/Project.toml
@@ -18,11 +18,13 @@ ConstructionBaseStaticArraysExt = "StaticArrays"
 IntervalSets = "0.5, 0.6, 0.7"
 StaticArrays = "1"
 julia = "1"
+LinearAlgebra = "<0.0.1,1"
 
 [extras]
 IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
 [targets]
-test = ["IntervalSets","StaticArrays","Test"]
+test = ["IntervalSets","LinearAlgebra","StaticArrays","Test"]
diff --git a/ext/ConstructionBaseLinearAlgebraExt.jl b/ext/ConstructionBaseLinearAlgebraExt.jl
new file mode 100644
index 0000000..9a06bf1
--- /dev/null
+++ b/ext/ConstructionBaseLinearAlgebraExt.jl
@@ -0,0 +1,46 @@
+module ConstructionBaseLinearAlgebraExt
+
+import ConstructionBase
+import LinearAlgebra
+
+### Tridiagonal
+
+function tridiagonal_constructor(dl::V, d::V, du::V) where {V<:AbstractVector{T}} where T
+    LinearAlgebra.Tridiagonal{T,V}(dl, d, du)
+end
+function tridiagonal_constructor(dl::V, d::V, du::V, du2::V) where {V<:AbstractVector{T}} where T
+    LinearAlgebra.Tridiagonal{T,V}(dl, d, du, du2)
+end
+
+# `du2` may be undefined, so we need a custom `getfields` that checks `isdefined`
+function ConstructionBase.getfields(o::LinearAlgebra.Tridiagonal)
+    if isdefined(o, :du2)
+        (dl=o.dl, d=o.d, du=o.du, du2=o.du2)
+    else
+        (dl=o.dl, d=o.d, du=o.du)
+    end
+end
+
+ConstructionBase.constructorof(::Type{<:LinearAlgebra.Tridiagonal}) = tridiagonal_constructor
+
+### Cholesky
+
+ConstructionBase.setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple{()}) = C
+
+function ConstructionBase.setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple{(:L,),<:Tuple{<:LinearAlgebra.LowerTriangular}})
+    return LinearAlgebra.Cholesky(C.uplo === 'U' ? copy(patch.L.data') : patch.L.data, C.uplo, C.info)
+end
+function ConstructionBase.setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple{(:U,),<:Tuple{<:LinearAlgebra.UpperTriangular}})
+    return LinearAlgebra.Cholesky(C.uplo === 'L' ? copy(patch.U.data') : patch.U.data, C.uplo, C.info)
+end
+function ConstructionBase.setproperties(
+    C::LinearAlgebra.Cholesky,
+    patch::NamedTuple{(:UL,),<:Tuple{<:Union{LinearAlgebra.LowerTriangular,LinearAlgebra.UpperTriangular}}}
+)
+    return LinearAlgebra.Cholesky(patch.UL.data, C.uplo, C.info)
+end
+function ConstructionBase.setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple)
+    throw(ArgumentError("Invalid patch for `Cholesky`: $(patch)"))
+end
+
+end #module
\ No newline at end of file
diff --git a/src/ConstructionBase.jl b/src/ConstructionBase.jl
index c0d1236..d29c18f 100644
--- a/src/ConstructionBase.jl
+++ b/src/ConstructionBase.jl
@@ -211,4 +211,7 @@ end
 include("nonstandard.jl")
 include("functions.jl")
 
+#unconditionally include the extension for now
+include("../ext/ConstructionBaseLinearAlgebraExt.jl")
+
 end # module
diff --git a/src/nonstandard.jl b/src/nonstandard.jl
index 4b114a7..e1b839b 100644
--- a/src/nonstandard.jl
+++ b/src/nonstandard.jl
@@ -1,4 +1,3 @@
-using LinearAlgebra
 
 ### SubArray
 # `offset1` and `stride1` fields are calculated from parent indices.
@@ -28,24 +27,7 @@ end
 constructorof(::Type{<:PermutedDimsArray{<:Any,N,perm,iperm,<:Any}}) where {N,perm,iperm} =
     PermutedDimsArrayConstructor{N,perm,iperm}()
 
-### Tridiagonal
-function tridiagonal_constructor(dl::V, d::V, du::V) where {V<:AbstractVector{T}} where T
-    Tridiagonal{T,V}(dl, d, du)
-end
-function tridiagonal_constructor(dl::V, d::V, du::V, du2::V) where {V<:AbstractVector{T}} where T
-    Tridiagonal{T,V}(dl, d, du, du2)
-end
 
-# `du2` may be undefined, so we need a custom `getfields` that checks `isdefined`
-function getfields(o::Tridiagonal)
-    if isdefined(o, :du2)
-        (dl=o.dl, d=o.d, du=o.du, du2=o.du2) 
-    else
-        (dl=o.dl, d=o.d, du=o.du)
-    end
-end
-
-constructorof(::Type{<:LinearAlgebra.Tridiagonal}) = tridiagonal_constructor
 
 ### LinRange
 # `lendiv` is a calculated field
@@ -56,21 +38,3 @@ constructorof(::Type{<:LinRange}) = linrange_constructor
 ### Expr: args get splatted
 # ::Expr annotation is to make it type-stable on Julia 1.3-
 constructorof(::Type{<:Expr}) = (head, args) -> Expr(head, args...)::Expr
-
-### Cholesky
-setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple{()}) = C
-function setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple{(:L,),<:Tuple{<:LinearAlgebra.LowerTriangular}})
-    return LinearAlgebra.Cholesky(C.uplo === 'U' ? copy(patch.L.data') : patch.L.data, C.uplo, C.info)
-end
-function setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple{(:U,),<:Tuple{<:LinearAlgebra.UpperTriangular}})
-    return LinearAlgebra.Cholesky(C.uplo === 'L' ? copy(patch.U.data') : patch.U.data, C.uplo, C.info)
-end
-function setproperties(
-    C::LinearAlgebra.Cholesky,
-    patch::NamedTuple{(:UL,),<:Tuple{<:Union{LinearAlgebra.LowerTriangular,LinearAlgebra.UpperTriangular}}}
-)
-    return LinearAlgebra.Cholesky(patch.UL.data, C.uplo, C.info)
-end
-function setproperties(C::LinearAlgebra.Cholesky, patch::NamedTuple)
-    throw(ArgumentError("Invalid patch for `Cholesky`: $(patch)"))
-end