Update 08-linear-algebra.md (DataTalksClub#241)

course-zoomcamp/01-intro/08-linear-algebra.md

@@ -7,6 +7,96 @@
 
 ## Notes
 
+### Linear Algebra Refresher
+* Vector operations
+* Multiplication
+  * Vector-vector multiplication
+  * Matrix-vector multiplication
+  * Matrix-matrix multiplication
+* Identity matrix
+* Inverse
+
+### Vector operations
+~~~~python
+u = np.array([2, 7, 5, 6])
+v = np.array([3, 4, 8, 6])
+
+# addition 
+u + v
+
+# subtraction 
+u - v
+
+# scalar multiplication 
+2 * v
+~~~~
+### Multiplication
+
+#####  Vector-vector multiplication
+
+~~~~python
+def vector_vector_multiplication(u, v):
+    assert u.shape[0] == v.shape[0]
+
+    n = u.shape[0]
+
+    result = 0.0
+
+    for i in range(n):
+        result = result + u[i] * v[i]
+
+    return result
+~~~~
+
+#####  Matrix-vector multiplication
+
+~~~~python
+def matrix_vector_multiplication(U, v):
+    assert U.shape[1] == v.shape[0]
+
+    num_rows = U.shape[0]
+
+    result = np.zeros(num_rows)
+
+    for i in range(num_rows):
+        result[i] = vector_vector_multiplication(U[i], v)
+
+    return result
+~~~~
+
+#####  Matrix-matrix multiplication
+
+~~~~python
+def matrix_matrix_multiplication(U, V):
+    assert U.shape[1] == V.shape[0]
+
+    num_rows = U.shape[0]
+    num_cols = V.shape[1]
+
+    result = np.zeros((num_rows, num_cols))
+
+    for i in range(num_cols):
+        vi = V[:, i]
+        Uvi = matrix_vector_multiplication(U, vi)
+        result[:, i] = Uvi
+
+    return result
+~~~~
+### Identity matrix
+
+~~~~python
+I = np.eye(3)
+~~~~
+### Inverse
+~~~~python
+V = np.array([
+    [1, 1, 2],
+    [0, 0.5, 1], 
+    [0, 2, 1],
+])
+inv = np.linalg.inv(V)
+~~~~
+
 
 Add notes here (PRs are welcome).