More matrix algorithms (#745)

* added matrix minor

* added matrix determinant

* added inverse,scalar multiply, identity, transpose

matrix/matrix_multiplication_addition.py

@@ -10,6 +10,8 @@ def add(matrix_a, matrix_b):
         matrix_c.append(list_1)
     return matrix_c
 
+def scalarMultiply(matrix , n):
+    return [[x * n for x in row] for row in matrix]
 
 def multiply(matrix_a, matrix_b):
     matrix_c = []
@@ -24,13 +26,50 @@ def multiply(matrix_a, matrix_b):
         matrix_c.append(list_1)
     return matrix_c
 
+def identity(n):
+    return [[int(row == column) for column in range(n)] for row in range(n)] 
+
+def transpose(matrix):
+    return map(list , zip(*matrix))
+
+def minor(matrix, row, column):
+    minor = matrix[:row] + matrix[row + 1:]
+    minor = [row[:column] + row[column + 1:] for row in minor]
+    return minor
+
+def determinant(matrix):
+    if len(matrix) == 1: return matrix[0][0]
+    
+    res = 0
+    for x in range(len(matrix)):
+        res += matrix[0][x] * determinant(minor(matrix , 0 , x)) * (-1) ** x
+    return res
+
+def inverse(matrix):
+    det = determinant(matrix)
+    if det == 0: return None
+
+    matrixMinor = [[] for _ in range(len(matrix))]
+    for i in range(len(matrix)):
+        for j in range(len(matrix)):
+            matrixMinor[i].append(determinant(minor(matrix , i , j)))
+    
+    cofactors = [[x * (-1) ** (row + col) for col, x in enumerate(matrixMinor[row])] for row in range(len(matrix))]
+    adjugate = transpose(cofactors)
+    return scalarMultiply(adjugate , 1/det)
 
 def main():
     matrix_a = [[12, 10], [3, 9]]
     matrix_b = [[3, 4], [7, 4]]
+    matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
+    matrix_d = [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
+
     print(add(matrix_a, matrix_b))
     print(multiply(matrix_a, matrix_b))
-
+    print(identity(5))
+    print(minor(matrix_c , 1 , 2))
+    print(determinant(matrix_b))
+    print(inverse(matrix_d))
 
 if __name__ == '__main__':
     main()