Matrix Determinant

Matrix/Matrix Determinant/Matrix-Determinant.py

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+def determinant(matrix): #Optimized solution
+    #your code here
+    result = 0
+    l = len(matrix)
+
+    #base case when length of matrix is 1
+    if l == 1:
+        return matrix[0][0]
+
+    #base case when length of matrix is 2
+    if l == 2:
+        return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]
+
+    #for length of matrix > 2
+    for j in range(0, l):
+        # create a sub matrix to find the determinant
+        if l!=2:
+            sub_matrix = []               
+            sub_matrix = [(row[0:j]+row[j+1:]) for row in matrix[1:]]
+        result = result + (-1)**j * matrix[0][j] * determinant(sub_matrix)
+    return result
+
+def det(matrix): #My (perhaps easier to understand) solution
+    if len(matrix)==1:      #Base Case
+        return matrix[0][0]
+    elif len(matrix)==2:    #Base Case
+        return matrix[0][0]*matrix[1][1] - matrix[1][0]*matrix[0][1]
+
+    else:
+        sub_m = [] #List containing sub matrixes
+        for z in range(len(matrix[0])):  
+            sub_m.append([])                                    #Create an empty list for all sub matrixes
+            for y in range(1,len(matrix)):
+                sub_m[z].append([])                             #Create rows for each sub matrix
+                for x in range(len(matrix[y])):
+                    if x != z:                                  #Check if sub matrix doesn't include the row of the multiplying value               
+                        sub_m[z][y-1].append(matrix[y][x])      #Append individual values to sub matrix
+        total = 0
+        for x in range(len(matrix[0])):     #cycle through matrix[0] values    
+            if matrix[0][x] != 0:
+                total += ((-1) ** x) * matrix[0][x] * det(sub_m[x])  #multiply them by the determinant of the sub matrix, creationg the recursion
+            else:                
+                continue
+        return total  #in the end returns the determninant
+
+
+

Matrix/Matrix Determinant/README.md

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+# Matrix Determinant
+
+The determinant of a matrix is a function of the entries of a square matrix.
+
+A Matrix Determinant can be calculated like so:
+
+![](https://www.chilimath.com/wp-content/uploads/2022/05/determinant-3x3-matrix-example-4.png)
+
+The input should be a 2 dimensional square array (of ```nxn``` size)
+
+The output should be an integer that is the matrix determinant
+
+# Recursive Method 
+
+1) Create a fuction that takes the matrix as the only argument
+2) Return the determinant for length 1x1 (```matrix[0][0]```) and 2x2 (```(matrix[0][0]*matrix[1][1]) - (matrix[1][0]*matrix[0][1])```) arrays directly
+3) Cycle trough the first row of the array (```x``` 1-4 for a length 4 array) and sum/subtract the product of each value and the determinant of the sub array (```x1*determinant - x2*determinant + x3*determinant - x4*determinant``` for a length 4 matrix) and repeat the cycle for the ensuing sub arrays of decreasing length