diff --git a/src/matrix.py b/src/matrix.py
index df98c10..611921e 100644
--- a/src/matrix.py
+++ b/src/matrix.py
@@ -87,6 +87,14 @@ class Matrix:
         """
         return Matrix(self.__data__.transpose())
 
+    def T(self):
+        """
+        Same as ``matrix.transpose()``
+
+        :return: see ``matrix.transpose()``
+        """
+        return self.transpose()
+
     def __eq__(self, other):
         """
         Return ``self==value``
diff --git a/src/vector.py b/src/vector.py
index b6caedc..c9403df 100644
--- a/src/vector.py
+++ b/src/vector.py
@@ -1,13 +1,17 @@
+import numpy
+
 from matrix import Matrix
 
 
 class Vector(Matrix):
-    def __init__(self, data: list | int):
+    def __init__(self, data):
         """
 
-        :type data: list | int
+        :type data: numpy.ndarray | list | int
         """
-        if isinstance(data, list):
+        if isinstance(data, numpy.ndarray):
+            super().__init__(data)
+        elif isinstance(data, list):
             super().__init__(data, (len(data), 1))
         elif isinstance(data, int):
             self.__init__([0] * data)
@@ -17,11 +21,16 @@ class Vector(Matrix):
     def get_dimension(self):
         return super().shape()[0]
 
+    def transpose(self):
+        return Vector(self.__data__.reshape(self.__shape__[1], self.__shape__[0]))
+
     def __mul__(self, other):
         if isinstance(other, Vector):
-            return (super().transpose().__mul__(other))[0][0]
+            if self.shape() == other.shape():
+                return Vector(self.__data__ * other.__data__)
+            return super().__mul__(other)[0][0]
         elif isinstance(other, int) or isinstance(other, float):
-            return super().__mul__(other)
+            return Vector(super().__mul__(other).__data__)
         else:
             raise ValueError("A vector can only be multiplied with an vector (dot product) or a scalar")
 
@@ -29,7 +38,19 @@ class Vector(Matrix):
         return self * other
 
     def norm(self, **kwargs):
+        """
+        Computes the 2-norm of the vector which is the Frobenius-Norm of a nx1 matrix.
+
+        :param kwargs: ignored
+        :return: the 2-norm of the vector
+        """
         return super().norm()
 
     def normalize(self):
+        """
+        A normalized vector has the length (norm) 1.
+        To achieve that the vector is divided by the norm of itself.
+
+        :return: the normalized vector
+        """
         return self / self.norm()
diff --git a/test/test_matrix.py b/test/test_matrix.py
index 758fce1..4d7c565 100644
--- a/test/test_matrix.py
+++ b/test/test_matrix.py
@@ -98,7 +98,7 @@ class TestMatrix(TestCase):
 
         self.assertNotEqual(m1, m2)
 
-    def test_should_transpose_matrix(self):
+    def test_should_transpose_square_matrix(self):
         data = [1, 2, 3, 4, 5, 6, 7, 8, 9]
         actual = Matrix(data, (3, 3))
 
@@ -106,6 +106,14 @@ class TestMatrix(TestCase):
         expected = [[1, 4, 7], [2, 5, 8], [3, 6, 9]]
         self.assertEqual(expected, actual)
 
+    def test_should_transpose_nonsquare_matrix(self):
+        data = [1, 2, 3, 4, 5, 6]
+        actual = Matrix(data, (2, 3))
+
+        actual = actual.transpose()
+        expected = [[1, 4], [2, 5], [3, 6]]
+        self.assertEqual(expected, actual)
+
     def test_should_negate_matrix(self):
         m = Matrix([1, 2, 3, 4], (2, 2))
 
diff --git a/test/test_serial.py b/test/test_serial.py
new file mode 100644
index 0000000..f657095
--- /dev/null
+++ b/test/test_serial.py
@@ -0,0 +1,216 @@
+import numpy as np
+
+from matrix import Matrix
+from vector import Vector
+
+np.random.seed(0)
+###############
+# Testing the vector class
+print("\n\nTesting the vector class -----------------------------------\n\n")
+###############
+
+### 1a Initialization
+print("Start 1a initialization")
+# from list
+x1 = [1, 2, 3, 4, 5]
+vec_x1 = Vector(x1)
+# from numpy array
+x2 = np.random.uniform(0, 1, 10000)
+vec_x2 = Vector(x2)
+print("End 1a\n")
+
+### 1b __str__ function, string representation
+print("Start 1b string representation")
+print(f"vec_x1 values: {str(vec_x1)}")
+print(f"vec_x2 values: {str(vec_x2)}")
+print("End 1b\n")
+
+### 1c shape and transpose
+print("Start 1c shape and transpose")
+# shape property of the vector
+print(f"vec_x1 has shape {vec_x1.shape()} | must be (5,1)")  # Hint: numpy.reshape
+# transposition (property) of the vector, only "cosmetic" change
+print(f"vec_x2.T() has shape {vec_x2.T().shape()} | must be (1,10000)")
+print(f"vec_x2.T().T() has shape {vec_x2.T().T().shape()} | must be (10000,1)")
+print("End 1c\n")
+
+### 1d addition and substraction
+print("Start 1d addition and substraction")
+# intitialization
+a = Vector([1, 3, 5, 7, 9])
+b = Vector([-2, 5, 1, 0, -3])
+# computation
+x = a + b
+print(f"a + b = {str(x)} | must be {np.array([1, 3, 5, 7, 9]) + np.array([-2, 5, 1, 0, -3])}")
+y = a - b
+print(f"a - b = {str(y)} | must be {np.array([1, 3, 5, 7, 9]) - np.array([-2, 5, 1, 0, -3])}")
+try:
+    x_false = a + b.T()
+except ValueError as e:
+    print("The correct result is this error: " + str(e))
+else:
+    print("It is required to raise a system error, e. g., ValueError, since dimensions mismatch!")
+try:
+    x_false = a - b.T()
+except ValueError as e:
+    print("The correct result is this error: " + str(e))
+else:
+    print("It is required to raise a system error, e. g., ValueError, since dimensions mismatch!")
+print("End 1d\n")
+
+### 1e multiplication 
+print("Start 1e multiplication")
+# intitialization
+a = Vector([1, 3, 5, 7, 9])
+b = Vector([-2, 5, 1, 0, -3])
+# computation with vectors
+x = a.T() * b  # scalar
+print(f"a.T() * b = {str(x)} | must be {np.sum(np.array([1, 3, 5, 7, 9]) * np.array([-2, 5, 1, 0, -3]))}")
+y = a * b  # vector
+print(f"a * b = {str(y)} | must be {np.array([1, 3, 5, 7, 9]) * np.array([-2, 5, 1, 0, -3])}")
+z = b * a.T()  # matrix
+print(f"b * a.T() = \n{str(z)} | must be \n{np.outer(np.array([-2, 5, 1, 0, -3]), np.array([1, 3, 5, 7, 9]))}")
+# computation with scalars
+x = a * 5
+print(f"a * 5 = {str(x)} | must be {np.array([1, 3, 5, 7, 9]) * 5}")
+y = 0.1 * b.T()
+print(f"0.1 * b.T()= {str(y)} | must be {0.1 * np.array([-2, 5, 1, 0, -3])}")
+print("End 1e\n")
+
+### 1f divison 
+print("Start 1f divison")
+# intitialization
+a = Vector([1, 3, 5, 7, 9])
+b = Vector([-2, 5, 1, 7, -3])
+# computation with vectors
+x = a / b
+print(f"a / b = str{x} | must be {np.array([1, 3, 5, 7, 9]) / np.array([-2, 5, 1, 7, -3])}")
+y = a / 5
+print(f"a / 5 = str{y} | must be {np.array([1, 3, 5, 7, 9]) / 5} ")
+print("End 1f\n")
+
+### 1g norm
+print("Start 1g norm")
+# intitialization
+a = Vector([1, 3, 5, 7, 9])
+a_norm, a_normalized = a.normalize()
+print(f"a_norm = {a_norm} | must be {np.linalg.norm([1, 3, 5, 7, 9])}")
+print(f"a_normalize = {str(a_normalized)} | must be {np.array([1, 3, 5, 7, 9]) / np.linalg.norm([1, 3, 5, 7, 9])}")
+print("End 1g\n")
+
+### 1h negation
+print("Start 1h negation")
+# intitialization
+a = Vector([1, 3, 5, 7, 9])
+x = -a
+print(f"-a = {str(x)} | must be {-np.array([1, 3, 5, 7, 9])}")
+print("End 1h\n")
+
+### 1i manipulation
+print("Start 1i manipulation")
+# intitialization
+a = Vector([1, 3, 5, 7, 9])
+print(
+    f"a[{str([1, 2, 4])}] = {str(a[1, 2, 4].reshape(3, ))} | must be {np.array([1, 3, 5, 7, 9]).reshape(5, 1)[np.array([1, 2, 4])].reshape(3, )}")
+a[1, 2, 4] = [-1, -1, -1]
+print(f"a = {str(a)} | must be {np.array([1, -1, -1, 5, 7, -1])}")
+print("End 1i\n")
+
+###############
+# Testing the matrix class
+print("\n\nTesting the matrix class -----------------------------------\n\n")
+###############
+
+### 1a Initialization
+print("Start 2a initialization")
+a_list = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 2 * np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])])
+A = Matrix(a_list)
+B = Matrix(structure="tridiagonal", given_size=11)
+c_list = [[(i + 1) / (index + 1) for index in range(10)] for i in range(10)]
+C = Matrix(c_list, given_shape=(10, 10))
+print("End 2a\n")
+
+### 1b __str__ function, string representation
+print("Start 2b string representation")
+# print(B.__str__(full = True))
+print(str(A))
+print(str(B))
+print(str(C))
+print("End 2b\n")
+
+### 1c shape and transpose
+print("Start 2c shape and transpose")
+# Initialization
+A = Matrix(np.array([i for i in range(12)]).reshape(-1, 1), given_shape=(4, 3))
+print(f"A has shape {A.shape()} | must be (4,3)")
+print(f"A.T() has shape {A.T().shape()} | must be (3,4)")
+print(f"A.T().T() has shape {A.T().T().shape()} | must be (4,3)")
+print("End 2c\n")
+
+### 1d addition and substraction
+print("Start 2d addition and substraction")
+# Initialization 
+A = Matrix(structure="diagonal", given_values=[3], offset=0, given_size=10)
+print(str(A))
+A21 = Matrix(structure="diagonal", given_values=[-1], offset=-1, given_size=10)
+print(str(A21))
+A12 = Matrix(structure="diagonal", given_values=[-1], offset=+1, given_size=10)
+print(str(A12))
+B = Matrix(structure="diagonal", given_values=[1], offset=0, given_size=10)
+print(str(B))
+# computation
+C = A + A21 + A12 - B
+print(str(C) + f"must be\n{Matrix(structure='tridiagonal', given_values=[-1, 2, -1], given_size=10)}")
+print(str(5 + A - 3))
+print("End 2d\n")
+
+### 1e multiplication 
+print("Start 2e multiplication")
+# initialization
+a_mat = [[(i0 + 1) / (i1 + 1) for i1 in range(3)] for i0 in range(10)]
+b_mat = [[(i0 + 1) / (i1 + 1) for i1 in range(10)] for i0 in range(3)]
+A = Matrix(a_mat)
+B = Matrix(b_mat)
+# computation
+# print(f"A * B =\n{str(A*B)}must be\n{str(np.round(np.array(a_mat) @ np.array(b_mat),decimals=3))}")
+print(f"Norm of (A*B - np.(A*B)) is {(A * B - Matrix(np.array(a_mat) @ np.array(b_mat))).norm()} | must be < 1e-8")
+# print(f"A.T() * A =\n{str(A.T()*A)}must be\n{str(np.round(np.array(a_mat).T@np.array(a_mat),decimals=3))}")
+print(
+    f"Norm of (A.T()*A - np(A.T()*A)) is {(A.T() * A - Matrix(np.array(a_mat).T @ np.array(a_mat))).norm()} | must be < 1e-8")
+# print(f"A * A.T() =\n{str(A*A.T())}must be\n{str(np.round(np.array(a_mat)@np.array(a_mat).T,decimals=3))}")
+print(
+    f"Norm of (A*A.T() - np(A*A.T())) is {(A * A.T() - Matrix(np.array(a_mat) @ np.array(a_mat).T)).norm()} | must be < 1e-8")
+# print(f"B.T() * A.T() =\n{str(B.T()*A.T())}must be\n{str(np.round(np.array(b_mat).T @ np.array(a_mat).T,decimals=3))}")
+print(
+    f"Norm of (B.T()*A.T() - np.(B.T()*A.T())) is {(B.T() * A.T() - Matrix(np.array(b_mat).T @ np.array(a_mat).T)).norm()} | must be < 1e-8")
+print("End 2e\n")
+
+### 1f divison 
+print("Start 2f divison")
+# initialization
+A = Matrix(a_mat)
+# computation
+print(f"Norm of (A/5 - np.(A/5)) is {(A / 5 - Matrix(np.array(a_mat) / 5)).norm()} | must be < 1e-8")
+print("End 2f\n")
+
+### 1g norm
+print("Start 2g norm")
+A = Matrix(structure="tridiagonal", given_size=50, given_values=[-1, 2, -1])
+print(f"Frobenius norm of tridiagonal matrix: {A.norm('frobenius')} | must be 17.263")
+print(f"Row sum norm of tridiagonal matrix: {A.norm('row sum')} | must be 2")
+print(f"Col sum norm of tridiagonal matrix: {A.norm('col sum')} | must be 2")
+print("End 2g\n")
+
+### 1h negation
+print("Start 2h negation")
+A = Matrix(structure="tridiagonal", given_size=50, given_values=[-1, 2, 1])
+print(f"Norm of (A + (-A)) is {(A + (-A)).norm('frobenius')} | must be < 1e-8")
+print("End 2h\n")
+
+### 1i manipulation
+print("Start 2i manipulation")
+A = Matrix(structure="tridiagonal", given_size=10, given_values=[-1, 2, 1])
+A[1, 1] = 4
+A[[1, 2, 3], 2] = [-5, -10, 100]
+print(str(A))
+print("End 2i\n")
diff --git a/test/test_vector.py b/test/test_vector.py
index 6b0f79f..7b2cc5c 100644
--- a/test/test_vector.py
+++ b/test/test_vector.py
@@ -22,6 +22,14 @@ class TestVector(TestCase):
 
         self.assertEqual(expected, actual)
 
+    def test_should_transpose_vector(self):
+        data = [1, 2, 3, 4, 5, 6]
+        actual = Vector(data)
+
+        actual = actual.transpose()
+        expected = [[1, 2, 3, 4, 5, 6]]
+        self.assertEqual(expected, actual)
+
     def test_should_neg_vector(self):
         v = Vector([1, 2])
 
@@ -96,12 +104,21 @@ class TestVector(TestCase):
 
         self.assertEqual(expected, actual)
 
-    def test_should_mul_vectors(self):
+    def test_should_mul_same_shape_vectors(self):
+        v1 = Vector([1, 2])
+        v2 = Vector([3, 4])
+
+        expected = Vector([3, 8])
+        actual = v1 * v2
+
+        self.assertEqual(expected, actual)
+
+    def test_should_mul_vectors_dot(self):
         v1 = Vector([1, 2])
         v2 = Vector([3, 4])
 
         expected = 11
-        actual = v1 * v2
+        actual = v1.T() * v2
 
         self.assertEqual(expected, actual)