diff --git a/matrix_math.py b/matrix_math.py
new file mode 100644
index 0000000..9f95253
--- /dev/null
+++ b/matrix_math.py
@@ -0,0 +1,83 @@
+import math
+
+class Vector:
+    def __init__(self, vector):
+        self.vector = vector
+
+
+    def shape(self):
+        if isinstance(self.vector[0], int):
+            return (len(self.vector), )
+
+
+    def __eq__(self, other):
+        return len(self.vector) == len(other.vector)
+
+
+    def __add__(self, other):
+        if self != other:
+            raise TypeError("Cannot add vector {} to vector {}.".format(
+                             other, self.vector))
+        else:
+            return [x + y for x, y in zip(self.vector, other.vector)]
+
+
+    def __sub__(self, other):
+        if self != other:
+            raise TypeError("Cannot subtract vector {} from vector {}.".format(
+                             other, self.vector))
+        else:
+            return [x - y for x, y in zip(self.vector, other.vector)]
+
+
+    def __mul__(self, scalar):
+        return [self.vector[i] * scalar for i in range(len(self.vector))]
+
+
+    def vector_dot(self, other):
+        if self != other:
+            raise TypeError
+        else:
+            return sum([self.vector[i] * other.vector[i] for i in range(len(self.vector))])
+
+
+    def magnitude(self):
+        return math.sqrt(sum([self.vector[i]**2 for i in range(len(self.vector))]))
+
+
+
+class Matrix:
+    def __init__(self, matrix):
+        self.matrix = matrix
+
+
+    def shape(self):
+        if isinstance(self.matrix[0], list):
+            return (len(self.matrix), len(self.matrix[1]))
+
+
+    def __eq__(self, other):
+        return len(self.matrix) == len(other.matrix[0])
+
+
+    def __add__(self, other):
+        if self != other:
+            raise TypeError("Cannot add matrix {} to matrix {}.".format(
+                             other.matrix, self.matrix))
+        else:
+            return [Vector(self.matrix[x]) + Vector(other.matrix[x])
+                    for x in range(len(self.matrix))]
+
+
+    def __mul__(self,other):
+        if isinstance(other, int):
+            return [Vector(i) * other for i in self.matrix]
+        elif isinstance(other, Vector):
+            return
+        elif isinstance(other, Matrix):
+            return
+
+
+    def transpose(self):
+        return [self.matrix[len(self.matrix) - j - 1][i]
+                for i, j in range(len(self.matrix))]
diff --git a/test_matrix_math.py b/test_matrix_math.py
new file mode 100644
index 0000000..ed66dbc
--- /dev/null
+++ b/test_matrix_math.py
@@ -0,0 +1,135 @@
+from matrix_math import *
+from nose.tools import raises
+
+
+m = Vector([3, 4])
+n = Vector([5, 0])
+
+v = Vector([1, 3, 0])
+w = Vector([0, 2, 4])
+u = Vector([1, 1, 1])
+y = Vector([10, 20, 30])
+z = Vector([0, 0, 0])
+
+
+def test_shape_vectors():
+    """shape should take a vector or matrix and return a tuple with the
+    number of rows (for a vector) or the number of rows and columns
+    (for a matrix.)"""
+    assert m.shape() == (2,)
+    assert v.shape() == (3,)
+    assert w.shape() == (3,)
+
+@raises(TypeError)
+def test_vectors_with_differing_length_cannot_be_added():
+    m + v
+    n + y
+
+def test_vector_add():
+    """
+    [a b]  + [c d]  = [a+c b+d]
+    Matrix + Matrix = Matrix
+    """
+    assert v + w == [1, 5, 4]
+    assert u + y == [11, 21, 31]
+    assert u == u
+
+@raises(TypeError)
+def test_vectors_with_differing_length_cannot_be_subtracted():
+    m - v
+    z - n
+
+def test_vector_sub():
+    """
+    [a b]  - [c d]  = [a-c b-d]
+    Matrix + Matrix = Matrix
+    """
+    assert v - w == [1, 1, -4]
+    assert w - v == [-1, -1, 4]
+    assert y  == y
+    assert w - u == [-1, 1, 3]
+
+def test_dot():
+    """
+    dot([a b], [c d])   = a * c + b * d
+    dot(Vector, Vector) = Scalar
+    """
+    assert Vector.vector_dot(w, y) == 160
+    assert Vector.vector_dot(m, n) == 15
+    assert Vector.vector_dot(u, z) == 0
+
+
+@raises(TypeError)
+def test_dot_checks_shapes():
+    """Shape rule: the vectors must be the same size."""
+    Vector.vector_dot(v, m)
+
+
+def test_vector_multiply():
+    """
+    [a b]  *  Z     = [a*Z b*Z]
+    Vector * Scalar = Vector
+    """
+    assert v * 0.5 == [0.5, 1.5, 0]
+    assert m * 2 == [6, 8]
+
+
+def test_magnitude():
+    """
+    magnitude([a b])  = sqrt(a^2 + b^2)
+    magnitude(Vector) = Scalar
+    """
+    assert m.magnitude() == 5
+    assert v.magnitude() == math.sqrt(10)
+    assert y.magnitude() == math.sqrt(1400)
+    assert z.magnitude() == 0
+
+
+A = Matrix([[1, 0, 0],
+           [0, 1, 0],
+           [0, 0, 1]])
+B = Matrix([[1, 2, 3],
+           [4, 5, 6],
+           [7, 8, 9]])
+C = Matrix([[1, 2],
+           [2, 1],
+           [1, 2]])
+D = Matrix([[1, 2, 3],
+           [3, 2, 1]])
+
+
+def test_shape_matrices():
+    """shape should take a vector or matrix and return a tuple with the
+    number of rows (for a vector) or the number of rows and columns
+    (for a matrix.)"""
+    assert A.shape() == (3, 3)
+    assert C.shape() == (3, 2)
+    assert D.shape() == (2, 3)
+
+
+def test_matrix_add():
+    """
+    [a b]  + [c d]  = [a+c b+d]
+    [w x]  + [y z]  = [w+y x+z]
+    Matrix + Matrix = Matrix
+    """
+    assert A + B == [[2, 2, 3],
+                     [4, 6, 6],
+                     [7, 8, 10]]
+
+def test_matrix_scalar_multiply():
+    """
+    [[a b]   *  Z   =   [[a*Z b*Z]
+     [c d]]              [c*Z d*Z]]
+    Matrix * Scalar = Matrix
+    """
+    assert C * 3 == [[3, 6],
+                     [6, 3],
+                     [3, 6]]
+
+
+def test_transpose():
+
+    assert A == [[0, 0, 1],
+                 [0, 1, 0],
+                 [1, 0, 0]]