diff --git a/numethods/linalg.py b/numethods/linalg.py
index af70b95..3dac7fc 100644
--- a/numethods/linalg.py
+++ b/numethods/linalg.py
@@ -21,6 +21,9 @@ class Vector:
     def copy(self) -> "Vector":
         return Vector(self.data[:])
 
+    def norm(self) -> Number:
+        return sum(abs(x) for x in self.data)
+
     def norm_inf(self) -> Number:
         return max(abs(x) for x in self.data) if self.data else 0.0
 
@@ -28,12 +31,14 @@ class Vector:
         return sum(x * x for x in self.data) ** 0.5
 
     def __add__(self, other: "Vector") -> "Vector":
-        assert len(self) == len(other)
-        return Vector(a + b for a, b in zip(self.data, other.data))
+        if len(self) != len(other):
+            raise ValueError("Vector dimensions must match for addition")
+        return Vector([a + b for a, b in zip(self.data, other.data)])
 
     def __sub__(self, other: "Vector") -> "Vector":
-        assert len(self) == len(other)
-        return Vector(a - b for a, b in zip(self.data, other.data))
+        if len(self) != len(other):
+            raise ValueError("Vector dimensions must match for subtraction")
+        return Vector([a - b for a, b in zip(self.data, other.data)])
 
     def __mul__(self, scalar: Number) -> "Vector":
         return Vector(scalar * x for x in self.data)
@@ -92,6 +97,50 @@ class Matrix:
     def col(self, j: int) -> Vector:
         return Vector(self.data[i][j] for i in range(self.m))
 
+    def norm(self) -> Number:
+        return (
+            max(sum(abs(self.data[i][j]) for i in range(self.m)) for j in range(self.n))
+            if self.n > 0
+            else 0.0
+        )
+
+    def norm_inf(self) -> Number:
+        return (
+            max(sum(abs(self.data[i][j]) for j in range(self.n)) for i in range(self.m))
+            if self.m > 0
+            else 0.0
+        )
+
+    def norm_fro(self) -> Number:
+        return (
+            sum(self.data[i][j] ** 2 for i in range(self.m) for j in range(self.n))
+            ** 0.5
+        )
+
+    def __add__(self, other: "Matrix") -> "Matrix":
+        if not isinstance(other, Matrix):
+            raise TypeError("Can only add Matrix with Matrix")
+        if self.m != other.m or self.n != other.n:
+            raise ValueError("Matrix dimensions must match for addition")
+        return Matrix(
+            [
+                [self.data[i][j] + other.data[i][j] for j in range(self.n)]
+                for i in range(self.m)
+            ]
+        )
+
+    def __sub__(self, other: "Matrix") -> "Matrix":
+        if not isinstance(other, Matrix):
+            raise TypeError("Can only subtract Matrix with Matrix")
+        if self.m != other.m or self.n != other.n:
+            raise ValueError("Matrix dimensions must match for subtraction")
+        return Matrix(
+            [
+                [self.data[i][j] - other.data[i][j] for j in range(self.n)]
+                for i in range(self.m)
+            ]
+        )
+
     def transpose(self) -> "Matrix":
         return Matrix([[self.data[i][j] for i in range(self.m)] for j in range(self.n)])