diff --git a/tests/linalg_tests.cpp b/tests/linalg_tests.cpp
index 0b6b31801..9841f03bf 100644
--- a/tests/linalg_tests.cpp
+++ b/tests/linalg_tests.cpp
@@ -16,33 +16,34 @@ TEST_CASE("[mlx.core.linalg.norm] no ord") {
   array arr_three_d = reshape(arange(18), {2, 3, 3});
 
   CHECK(array_equal(norm(arr_one_d), array(sqrt(1 + 4 + 9))).item<bool>());
-  CHECK(array_equal(norm(arr_one_d, {0}), array(sqrt(1 + 4 + 9))).item<bool>());
+  CHECK(array_equal(norm(arr_one_d, {0}, false), array(sqrt(1 + 4 + 9)))
+            .item<bool>());
   CHECK(array_equal(
-            norm(arr_two_d),
+            norm(arr_two_d, {}, false),
             array(sqrt(
                 0 + 1 + 2 * 2 + 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6 + 7 * 7 + 8 * 8)))
             .item<bool>());
   CHECK(array_equal(
-            norm(arr_two_d, {0}),
+            norm(arr_two_d, {0}, false),
             array(
                 {sqrt(0 + 3 * 3 + 6 * 6),
                  sqrt(1 + 4 * 4 + 7 * 7),
                  sqrt(2 * 2 + 5 * 5 + 8 * 8)}))
             .item<bool>());
   CHECK(array_equal(
-            norm(arr_two_d, {1}),
+            norm(arr_two_d, {1}, false),
             array(
                 {sqrt(0 + 1 + 2 * 2),
                  sqrt(3 * 3 + 4 * 4 + 5 * 5),
                  sqrt(6 * 6 + 7 * 7 + 8 * 8)}))
             .item<bool>());
   CHECK(array_equal(
-            norm(arr_two_d, {0, 1}),
+            norm(arr_two_d, {0, 1}, false),
             array(sqrt(
                 0 + 1 + 2 * 2 + 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6 + 7 * 7 + 8 * 8)))
             .item<bool>());
   CHECK(array_equal(
-            norm(arr_three_d, {2}),
+            norm(arr_three_d, {2}, false),
             array(
                 {
                     sqrt(0 + 1 + 2 * 2),
@@ -55,7 +56,7 @@ TEST_CASE("[mlx.core.linalg.norm] no ord") {
                 {2, 3}))
             .item<bool>());
   CHECK(array_equal(
-            norm(arr_three_d, {1}),
+            norm(arr_three_d, {1}, false),
             array(
                 {
                     sqrt(0 + 3 * 3 + 6 * 6),
@@ -68,7 +69,7 @@ TEST_CASE("[mlx.core.linalg.norm] no ord") {
                 {2, 3}))
             .item<bool>());
   CHECK(array_equal(
-            norm(arr_three_d, {0}),
+            norm(arr_three_d, {0}, false),
             array(
                 {
                     sqrt(0 + 9 * 9),
@@ -84,7 +85,7 @@ TEST_CASE("[mlx.core.linalg.norm] no ord") {
                 {3, 3}))
             .item<bool>());
   CHECK(array_equal(
-            norm(arr_three_d, {1, 2}),
+            norm(arr_three_d, {1, 2}, false),
             array(
                 {sqrt(
                      0 + 1 + 2 * 2 + 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6 + 7 * 7 +
@@ -94,4 +95,212 @@ TEST_CASE("[mlx.core.linalg.norm] no ord") {
                      15 * 15 + 16 * 16 + 17 * 17)},
                 {2}))
             .item<bool>());
+}
+
+TEST_CASE("[mlx.core.linalg.norm] double ord") {
+  array arr_one_d({1, 2, 3});
+  array arr_two_d = reshape(arange(9), {3, 3});
+  array arr_three_d = reshape(arange(18), {2, 3, 3});
+
+  CHECK(array_equal(norm(arr_one_d, 2.0), array(sqrt(1 + 4 + 9))).item<bool>());
+  CHECK(array_equal(norm(arr_one_d, 1.0), array(1 + 2 + 3)).item<bool>());
+  CHECK(array_equal(norm(arr_one_d, 0.0), array(3)).item<bool>());
+
+  CHECK(array_equal(norm(arr_one_d, 2.0, {0}, false), array(sqrt(1 + 4 + 9)))
+            .item<bool>());
+  CHECK(array_equal(
+            norm(arr_two_d, 2.0, {0}, false),
+            array(
+                {sqrt(0 + 3 * 3 + 6 * 6),
+                 sqrt(1 + 4 * 4 + 7 * 7),
+                 sqrt(2 * 2 + 5 * 5 + 8 * 8)}))
+            .item<bool>());
+  CHECK(array_equal(
+            norm(arr_two_d, 2.0, {1}, false),
+            array(
+                {sqrt(0 + 1 + 2 * 2),
+                 sqrt(3 * 3 + 4 * 4 + 5 * 5),
+                 sqrt(6 * 6 + 7 * 7 + 8 * 8)}))
+            .item<bool>());
+  CHECK(array_equal(
+            norm(arr_three_d, 2.0, {2}, false),
+            array(
+                {
+                    sqrt(0 + 1 + 2 * 2),
+                    sqrt(3 * 3 + 4 * 4 + 5 * 5),
+                    sqrt(6 * 6 + 7 * 7 + 8 * 8),
+                    sqrt(9 * 9 + 10 * 10 + 11 * 11),
+                    sqrt(12 * 12 + 13 * 13 + 14 * 14),
+                    sqrt(15 * 15 + 16 * 16 + 17 * 17),
+                },
+                {2, 3}))
+            .item<bool>());
+  CHECK(array_equal(
+            norm(arr_three_d, 2.0, {1}, false),
+            array(
+                {
+                    sqrt(0 + 3 * 3 + 6 * 6),
+                    sqrt(1 + 4 * 4 + 7 * 7),
+                    sqrt(2 * 2 + 5 * 5 + 8 * 8),
+                    sqrt(9 * 9 + 12 * 12 + 15 * 15),
+                    sqrt(10 * 10 + 13 * 13 + 16 * 16),
+                    sqrt(11 * 11 + 14 * 14 + 17 * 17),
+                },
+                {2, 3}))
+            .item<bool>());
+  CHECK(array_equal(
+            norm(arr_three_d, 2.0, {0}, false),
+            array(
+                {
+                    sqrt(0 + 9 * 9),
+                    sqrt(1 + 10 * 10),
+                    sqrt(2 * 2 + 11 * 11),
+                    sqrt(3 * 3 + 12 * 12),
+                    sqrt(4 * 4 + 13 * 13),
+                    sqrt(5 * 5 + 14 * 14),
+                    sqrt(6 * 6 + 15 * 15),
+                    sqrt(7 * 7 + 16 * 16),
+                    sqrt(8 * 8 + 17 * 17),
+                },
+                {3, 3}))
+            .item<bool>());
+
+  CHECK(allclose(
+            norm(arr_three_d, 3.0, {0}),
+            array(
+                {9.,
+                 10.00333222,
+                 11.02199456,
+                 12.06217728,
+                 13.12502645,
+                 14.2094363,
+                 15.31340617,
+                 16.43469751,
+                 17.57113899},
+                {3, 3}))
+            .item<bool>());
+  CHECK(
+      allclose(
+          norm(arr_three_d, 3.0, {1}),
+          array(
+              {6.24025147, 7.41685954, 8.6401226, 18., 19.39257164, 20.7915893},
+              {2, 3}))
+          .item<bool>());
+  CHECK(allclose(
+            norm(arr_three_d, 3.0, {2}),
+            array(
+                {2.08008382,
+                 6.,
+                 10.23127655,
+                 14.5180117,
+                 18.82291607,
+                 23.13593104},
+                {2, 3}))
+            .item<bool>());
+  CHECK(allclose(
+            norm(arr_three_d, 0.0, {0}),
+            array({1., 2., 2., 2., 2., 2., 2., 2., 2.}, {3, 3}))
+            .item<bool>());
+  CHECK(
+      allclose(
+          norm(arr_three_d, 0.0, {1}), array({2., 3., 3., 3., 3., 3.}, {2, 3}))
+          .item<bool>());
+  CHECK(
+      allclose(
+          norm(arr_three_d, 0.0, {2}), array({2., 3., 3., 3., 3., 3.}, {2, 3}))
+          .item<bool>());
+  CHECK(allclose(
+            norm(arr_three_d, 1.0, {0}),
+            array({9., 11., 13., 15., 17., 19., 21., 23., 25.}, {3, 3}))
+            .item<bool>());
+  CHECK(allclose(
+            norm(arr_three_d, 1.0, {1}),
+            array({9., 12., 15., 36., 39., 42.}, {2, 3}))
+            .item<bool>());
+  CHECK(allclose(
+            norm(arr_three_d, 1.0, {2}),
+            array({3., 12., 21., 30., 39., 48.}, {2, 3}))
+            .item<bool>());
+
+  CHECK(allclose(norm(arr_two_d, 1.0, {0, 1}), array({15.0})).item<bool>());
+  CHECK(allclose(norm(arr_two_d, 1.0, {1, 0}), array({21.0})).item<bool>());
+  CHECK(allclose(norm(arr_two_d, -1.0, {0, 1}), array({9.0})).item<bool>());
+  CHECK(allclose(norm(arr_two_d, -1.0, {1, 0}), array({3.0})).item<bool>());
+
+  CHECK(allclose(norm(arr_two_d, 1.0, {0, 1}, true), array({15.0}, {1, 1}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_two_d, 1.0, {1, 0}, true), array({21.0}, {1, 1}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_two_d, -1.0, {0, 1}, true), array({9.0}, {1, 1}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_two_d, -1.0, {1, 0}, true), array({3.0}, {1, 1}))
+            .item<bool>());
+
+  CHECK(array_equal(norm(arr_two_d, -1.0, {-2, -1}, false), array(9.0))
+            .item<bool>());
+  CHECK(array_equal(norm(arr_two_d, 1.0, {-2, -1}, false), array(15.0))
+            .item<bool>());
+  //
+  CHECK(allclose(norm(arr_three_d, 1.0, {0, 1}), array({21., 23., 25.}))
+            .item<bool>());
+  CHECK(
+      allclose(norm(arr_three_d, 1.0, {1, 2}), array({15., 42.})).item<bool>());
+  CHECK(allclose(norm(arr_three_d, -1.0, {0, 1}), array({9., 11., 13.}))
+            .item<bool>());
+  CHECK(
+      allclose(norm(arr_three_d, -1.0, {1, 2}), array({9., 36.})).item<bool>());
+  CHECK(allclose(norm(arr_three_d, -1.0, {1, 0}), array({9., 12., 15.}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_three_d, -1.0, {2, 1}), array({3, 30})).item<bool>());
+  CHECK(allclose(norm(arr_three_d, -1.0, {1, 2}), array({9, 36})).item<bool>());
+}
+
+TEST_CASE("[mlx.core.linalg.norm] string ord") {
+  array arr_one_d({1, 2, 3});
+  array arr_two_d = reshape(arange(9), {3, 3});
+  array arr_three_d = reshape(arange(18), {2, 3, 3});
+
+  CHECK(allclose(norm(arr_one_d, "inf", {}), array({3.0})).item<bool>());
+  CHECK(allclose(norm(arr_one_d, "-inf", {}), array({1.0})).item<bool>());
+
+  CHECK(allclose(norm(arr_two_d, "f", {0, 1}), array({14.2828568570857}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_two_d, "fro", {0, 1}), array({14.2828568570857}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_two_d, "inf", {0, 1}), array({21.0})).item<bool>());
+  CHECK(allclose(norm(arr_two_d, "-inf", {0, 1}), array({3.0})).item<bool>());
+
+  CHECK(allclose(
+            norm(arr_three_d, "fro", {0, 1}),
+            array({22.24859546, 24.31049156, 26.43860813}))
+            .item<bool>());
+  CHECK(allclose(
+            norm(arr_three_d, "fro", {1, 2}), array({14.28285686, 39.7617907}))
+            .item<bool>());
+  CHECK(allclose(
+            norm(arr_three_d, "f", {0, 1}),
+            array({22.24859546, 24.31049156, 26.43860813}))
+            .item<bool>());
+  CHECK(allclose(
+            norm(arr_three_d, "f", {1, 0}),
+            array({22.24859546, 24.31049156, 26.43860813}))
+            .item<bool>());
+  CHECK(
+      allclose(norm(arr_three_d, "f", {1, 2}), array({14.28285686, 39.7617907}))
+          .item<bool>());
+  CHECK(
+      allclose(norm(arr_three_d, "f", {2, 1}), array({14.28285686, 39.7617907}))
+          .item<bool>());
+  CHECK(allclose(norm(arr_three_d, "inf", {0, 1}), array({36., 39., 42.}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_three_d, "inf", {1, 2}), array({21., 48.}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_three_d, "-inf", {0, 1}), array({9., 12., 15.}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_three_d, "-inf", {1, 2}), array({3., 30.}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_three_d, "-inf", {1, 0}), array({9., 11., 13.}))
+            .item<bool>());
+  CHECK(allclose(norm(arr_three_d, "-inf", {2, 1}), array({9., 36.}))
+            .item<bool>());
 }
\ No newline at end of file