diff --git a/Project.toml b/Project.toml
index e42c704..f82dce3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NamedDims"
 uuid = "356022a1-0364-5f58-8944-0da4b18d706f"
 authors = ["Invenia Technical Computing Corporation"]
-version = "0.2.40"
+version = "0.2.41"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
diff --git a/src/functions_linearalgebra.jl b/src/functions_linearalgebra.jl
index caa1c93..310b29d 100644
--- a/src/functions_linearalgebra.jl
+++ b/src/functions_linearalgebra.jl
@@ -118,3 +118,39 @@ function Base.getproperty(
         return inner
     end
 end
+
+function LinearAlgebra.:\(
+    fact::NamedFactorization{L,T,F}, nda::NamedDimsArray{W}
+) where {L,T,F<:Factorization{T},W}
+    n1, n2 = L
+    n1 != W[1] && throw(
+        DimensionMismatch(
+            "Mismatched dimensions with factorization: $L and NamedDimsArray: $W"
+        ),
+    )
+    return NamedDimsArray{(n2,)}(LinearAlgebra.:\(parent(fact), parent(nda)))
+end
+
+function LinearAlgebra.:\(
+    fact::NamedFactorization{L,T,F}, nda::AbstractVector
+) where {L,T,F<:Factorization{T}}
+    n1, n2 = L
+    return NamedDimsArray{(n2,)}(LinearAlgebra.:\(parent(fact), nda))
+end
+
+# Specialised routines for \ often do in-place ops that result in the nameddim populated from B
+# Leading to an incorrect named-dim
+# We also unname here because that handles wrapper types
+for S in (UpperTriangular, LowerTriangular)
+    @eval begin
+        function LinearAlgebra.:\(
+            A::$S{T,<:NamedDimsArray{L}}, B::AbstractVector
+        ) where {L,T}
+            n1, n2 = L
+            return NamedDimsArray{(n2,)}(LinearAlgebra.:\($S(unname(A)), parent(B)))
+        end
+    end
+end
+
+# Diagonal on a nameddim presently loses its nameddimsness. So just pass through for now.
+LinearAlgebra.:\(A::Diagonal, B::NamedDimsArray) = LinearAlgebra.:\(A, parent(B))
diff --git a/src/name_operations.jl b/src/name_operations.jl
index a5283ee..eb8e96a 100644
--- a/src/name_operations.jl
+++ b/src/name_operations.jl
@@ -41,9 +41,17 @@ Return the input array `A` without any dimension names.
 
 For `NamedDimsArray`s this returns the parent array, equivalent to calling `parent`, but for
 anything else it simply returns the input.
+
+Supports some LinearAlgebra wrappers LowerTriangular, UpperTriangular such that
+`unname(x::UpperTriangular{T, <:NamedDimsArray}) == unname(parent(x))
+
 """
 unname(x::NamedDimsArray) = parent(x)
 unname(x) = x
+# Unwrap LinearAlgebra wrappers 
+for W in (LowerTriangular, UpperTriangular)
+    @eval unname(x::$W{T,<:NamedDimsArray}) where {T} = unname(parent(x))
+end
 
 """
     dimnames(A) -> Tuple
diff --git a/test/functions_linearalgebra.jl b/test/functions_linearalgebra.jl
index 454fece..13ebd29 100644
--- a/test/functions_linearalgebra.jl
+++ b/test/functions_linearalgebra.jl
@@ -1,3 +1,4 @@
+using Test: approx_full
 using LinearAlgebra
 using NamedDims
 using NamedDims: dimnames
@@ -139,5 +140,31 @@ end
 @testset "#164 factorization eltype not same as input eltype" begin
     # https://github.com/invenia/NamedDims.jl/issues/164
     nda = NamedDimsArray{(:foo, :bar)}([1 2 3; 4 5 6; 7 8 9])  # Int eltype
-    @test qr(nda) isa NamedDims.NamedFactorization{(:foo, :bar), Float64}
+    @test qr(nda) isa NamedDims.NamedFactorization{(:foo, :bar),Float64}
+end
+
+@testset "LinearAlgebra.:ldiv " begin
+    r1 = [2 3 5; 7 11 13; 17 19 23]
+    r2 = r1[:, 1:2]
+    b = [29, 31, 37]
+    b_nda = NamedDimsArray{(:foo,)}(b)
+
+    for A in (r1, r2)
+        (m, n) = size(A)
+        issquare = m == n
+        fn = issquare ? (identity, triu, tril, Diagonal) : (identity,)
+        for f in fn
+            for B in (b_nda, b)
+                nda = NamedDimsArray{(:foo, :bar)}(f(A))
+                x = nda \ B
+                @test parent(x) ≈ f(A) \ parent(B)
+                # NOTE: Diagonal loses NamedDimness so specialcase
+                f != Diagonal && @test dimnames(x) == (:bar,)
+            end
+        end
+    end
+
+    @test_throws DimensionMismatch (\)(
+        NamedDimsArray{(:A, :B)}(r1), NamedDimsArray{(:NotA,)}(b)
+    )
 end
diff --git a/test/name_operations.jl b/test/name_operations.jl
index 870901a..e56819a 100644
--- a/test/name_operations.jl
+++ b/test/name_operations.jl
@@ -1,11 +1,17 @@
+using LinearAlgebra: LowerTriangular, UpperTriangular
+
 @testset "unname" begin
     for orig in ([1 2; 3 4], spzeros(2, 2))
         @test unname(NamedDimsArray(orig, (:x, :y))) === orig
         @test unname(orig) === orig
     end
-    @test unname((1,2,3)) === (1,2,3)
-end
+    @test unname((1, 2, 3)) === (1, 2, 3)
 
+    for wrapper in (LowerTriangular, UpperTriangular)
+        orig = [1 2; 3 4]
+        @test unname(wrapper(NamedDimsArray(orig, (:x, :y)))) === orig
+    end
+end
 
 @testset "dimnames" begin
     nda = NamedDimsArray([10 20; 30 40], (:x, :y))