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 operationsimport numpy# initializing matricesx = numpy.array([[1, 2], [4, 5]])y = numpy.array([[7, 8], [9, 10]])# using add() to add matricesprint ("The element wise addition of matrix is : ")print (numpy.add(x,y))# using subtract() to subtract matricesprint ("The element wise subtraction of matrix is : ")print (numpy.subtract(x,y))# using divide() to divide matricesprint ("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 operationsimport numpy# initializing matricesx = numpy.array([[1, 2], [4, 5]])y = numpy.array([[7, 8], [9, 10]])# using multiply() to multiply matrices element wiseprint ("The element wise multiplication of matrix is : ")print (numpy.multiply(x,y))# using dot() to multiply matricesprint ("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 operationsimport numpy# initializing matricesx = numpy.array([[1, 2], [4, 5]])y = numpy.array([[7, 8], [9, 10]])# using sqrt() to print the square root of matrixprint ("The element wise square root is : ")print (numpy.sqrt(x))# using sum() to print summation of all elements of matrixprint ("The summation of all matrix element is : ")print (numpy.sum(y))# using sum(axis=0) to print summation of all columns of matrixprint ("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 matrixprint ("The row wise summation of all matrix is : ")print (numpy.sum(y,axis=1))# using "T" to transpose the matrixprint ("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 additionC = [[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 subtractionD = [[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 divisionE = [[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)
