diff --git a/test/mooncake/eig.jl b/test/mooncake/eig.jl
index 2e8a8606..7f0a792f 100644
--- a/test/mooncake/eig.jl
+++ b/test/mooncake/eig.jl
@@ -15,5 +15,7 @@ for T in (BLASFloats..., GenericFloats...)
     TestSuite.seed_rng!(123)
     if !is_buildkite
         TestSuite.test_mooncake_eig(T, (m, m); atol = m * m * TestSuite.precision(T), rtol = m * m * TestSuite.precision(T))
+        AT = Diagonal{T, Vector{T}}
+        TestSuite.test_mooncake_eig(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
     end
 end
diff --git a/test/mooncake/eigh.jl b/test/mooncake/eigh.jl
index 5528af0f..38f0b82e 100644
--- a/test/mooncake/eigh.jl
+++ b/test/mooncake/eigh.jl
@@ -15,5 +15,7 @@ for T in (BLASFloats..., GenericFloats...)
     TestSuite.seed_rng!(123)
     if !is_buildkite
         TestSuite.test_mooncake_eigh(T, (m, m); atol = m * m * TestSuite.precision(T), rtol = m * m * TestSuite.precision(T))
+        AT = Diagonal{T, Vector{T}}
+        TestSuite.test_mooncake_eigh(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
     end
 end
diff --git a/test/mooncake/lq.jl b/test/mooncake/lq.jl
index 6c9f8fd4..f95a4832 100644
--- a/test/mooncake/lq.jl
+++ b/test/mooncake/lq.jl
@@ -15,5 +15,9 @@ for T in (BLASFloats..., GenericFloats...), n in (17, m, 23)
     TestSuite.seed_rng!(123)
     if !is_buildkite
         TestSuite.test_mooncake_lq(T, (m, n); atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        if m == n
+            AT = Diagonal{T, Vector{T}}
+            TestSuite.test_mooncake_lq(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        end
     end
 end
diff --git a/test/mooncake/orthnull.jl b/test/mooncake/orthnull.jl
index 6f8dac9a..5e7db0ac 100644
--- a/test/mooncake/orthnull.jl
+++ b/test/mooncake/orthnull.jl
@@ -15,5 +15,9 @@ for T in (BLASFloats..., GenericFloats...), n in (17, m, 23)
     TestSuite.seed_rng!(123)
     if !is_buildkite
         TestSuite.test_mooncake_orthnull(T, (m, n); atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        if m == n
+            AT = Diagonal{T, Vector{T}}
+            TestSuite.test_mooncake_orthnull(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        end
     end
 end
diff --git a/test/mooncake/polar.jl b/test/mooncake/polar.jl
index 9e4e366e..4386854d 100644
--- a/test/mooncake/polar.jl
+++ b/test/mooncake/polar.jl
@@ -17,5 +17,10 @@ for T in (BLASFloats..., GenericFloats...), n in (17, m, 23)
         atol = rtol = m * n * TestSuite.precision(T)
         m >= n && TestSuite.test_mooncake_left_polar(T, (m, n); atol, rtol)
         n >= m && TestSuite.test_mooncake_right_polar(T, (m, n); atol, rtol)
+        if m == n
+            AT = Diagonal{T, Vector{T}}
+            TestSuite.test_mooncake_left_polar(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+            TestSuite.test_mooncake_right_polar(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        end
     end
 end
diff --git a/test/mooncake/qr.jl b/test/mooncake/qr.jl
index 9ffc4798..f18971e7 100644
--- a/test/mooncake/qr.jl
+++ b/test/mooncake/qr.jl
@@ -15,5 +15,9 @@ for T in (BLASFloats..., GenericFloats...), n in (17, m, 23)
     TestSuite.seed_rng!(123)
     if !is_buildkite
         TestSuite.test_mooncake_qr(T, (m, n); atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        if m == n
+            AT = Diagonal{T, Vector{T}}
+            TestSuite.test_mooncake_qr(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        end
     end
 end
diff --git a/test/mooncake/svd.jl b/test/mooncake/svd.jl
index 982ec040..22e55483 100644
--- a/test/mooncake/svd.jl
+++ b/test/mooncake/svd.jl
@@ -15,5 +15,9 @@ for T in (BLASFloats..., GenericFloats...), n in (17, m, 23)
     TestSuite.seed_rng!(123)
     if !is_buildkite
         TestSuite.test_mooncake_svd(T, (m, n); atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        if m == n
+            AT = Diagonal{T, Vector{T}}
+            TestSuite.test_mooncake_svd(AT, m; atol = m * n * TestSuite.precision(T), rtol = m * n * TestSuite.precision(T))
+        end
     end
 end