Matrix manipulation in Python

In python matrix can be implemented as 2D list or 2D Array. Forming matrix from latter, gives the additional functionalities for performing various operations in matrix. These operations and array are defines in module “numpy“. 

Operation on Matrix :

• 1. add() :- This function is used to perform element wise matrix addition. 
• 2. subtract() :- This function is used to perform element wise matrix subtraction. 
• 3. divide() :- This function is used to perform element wise matrix division. 

Implementation:

Python

# Python code to demonstrate matrix operations
# add(), subtract() and divide()

# importing numpy for matrix operations
import numpy

# initializing matrices
x = numpy.array([[1, 2], [4, 5]])
y = numpy.array([[7, 8], [9, 10]])

# using add() to add matrices
print ("The element wise addition of matrix is : ")
print (numpy.add(x,y))

# using subtract() to subtract matrices
print ("The element wise subtraction of matrix is : ")
print (numpy.subtract(x,y))

# using divide() to divide matrices
print ("The element wise division of matrix is : ")
print (numpy.divide(x,y))

Output :

The element wise addition of matrix is : 
[[ 8 10]
 [13 15]]
The element wise subtraction of matrix is : 
[[-6 -6]
 [-5 -5]]
The element wise division of matrix is : 
[[ 0.14285714  0.25      ]
 [ 0.44444444  0.5       ]]

• 4. multiply() :- This function is used to perform element wise matrix multiplication. 
• 5. dot() :- This function is used to compute the matrix multiplication, rather than element wise multiplication. 

Python

# Python code to demonstrate matrix operations
# multiply() and dot()

# importing numpy for matrix operations
import numpy

# initializing matrices
x = numpy.array([[1, 2], [4, 5]])
y = numpy.array([[7, 8], [9, 10]])

# using multiply() to multiply matrices element wise
print ("The element wise multiplication of matrix is : ")
print (numpy.multiply(x,y))

# using dot() to multiply matrices
print ("The product of matrices is : ")
print (numpy.dot(x,y))

Output :

The element wise multiplication of matrix is : 
[[ 7 16]
 [36 50]]
The product of matrices is : 
[[25 28]
 [73 82]]

• 6. sqrt() :- This function is used to compute the square root of each element of matrix. 
• 7. sum(x,axis) :- This function is used to add all the elements in matrix. Optional “axis” argument computes the column sum if axis is 0 and row sum if axis is 1. 
• 8. “T” :- This argument is used to transpose the specified matrix. 

Implementation:

Python

# Python code to demonstrate matrix operations
# sqrt(), sum() and "T"

# importing numpy for matrix operations
import numpy

# initializing matrices
x = numpy.array([[1, 2], [4, 5]])
y = numpy.array([[7, 8], [9, 10]])

# using sqrt() to print the square root of matrix
print ("The element wise square root is : ")
print (numpy.sqrt(x))

# using sum() to print summation of all elements of matrix
print ("The summation of all matrix element is : ")
print (numpy.sum(y))

# using sum(axis=0) to print summation of all columns of matrix
print ("The column wise summation of all matrix  is : ")
print (numpy.sum(y,axis=0))

# using sum(axis=1) to print summation of all columns of matrix
print ("The row wise summation of all matrix  is : ")
print (numpy.sum(y,axis=1))

# using "T" to transpose the matrix
print ("The transpose of given matrix is : ")
print (x.T)

Output :

The element wise square root is : 
[[ 1.          1.41421356]
 [ 2.          2.23606798]]
The summation of all matrix element is : 
34
The column wise summation of all matrix  is : 
[16 18]
The row wise summation of all matrix  is : 
[15 19]
The transpose of given matrix is : 
[[1 4]
 [2 5]]

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Using nested loops:

Approach:

• Define matrices A and B.
• Get the number of rows and columns of the matrices using the len() function.
• Initialize matrices C, D, and E with zeros using nested loops or list comprehension.
• Use nested loops or list comprehension to perform the element-wise addition, subtraction, and division of matrices.
• Print the resulting matrices C, D, and E.

Python3

A = [[1,2],[4,5]]
B = [[7,8],[9,10]]
rows = len(A)
cols = len(A[0])

# Element wise addition
C = [[0 for i in range(cols)] for j in range(rows)]
for i in range(rows):
    for j in range(cols):
        C[i][j] = A[i][j] + B[i][j]
print("Addition of matrices: \n", C)

# Element wise subtraction
D = [[0 for i in range(cols)] for j in range(rows)]
for i in range(rows):
    for j in range(cols):
        D[i][j] = A[i][j] - B[i][j]
print("Subtraction of matrices: \n", D)

# Element wise division
E = [[0 for i in range(cols)] for j in range(rows)]
for i in range(rows):
    for j in range(cols):
        E[i][j] = A[i][j] / B[i][j]
print("Division of matrices: \n", E)

Output

Addition of matrices: 
 [[8, 10], [13, 15]]
Subtraction of matrices: 
 [[-6, -6], [-5, -5]]
Division of matrices: 
 [[0.14285714285714285, 0.25], [0.4444444444444444, 0.5]]

Time complexity: O(n^2)
Space complexity: O(n^2)