Matrix Operations : Creation of Matrix
The 2-D array in NumPy is called as Matrix. The following line of code is used to create the Matrix.
>>> import numpy as np #load the Library
>>> matrix = np.array( [ [ 4, 5, 6 ], [ 7, 8, 9 ], [ 10, 11, 12 ] ] )
>>> print(matrix)
[[ 4 5 6]
[ 7 8 9]
[10 11 12]]
>>>
Matrix Operations : Describing a Matrix
To describe a matrix we use matrix.shape
>>> matrix = np.array( [ [ 4, 5, 6 ], [ 7, 8, 9 ], [ 10, 11, 12 ] ] )
>>> print( matrix )
[[ 4 5 6]
[ 7 8 9]
[10 11 12]]
>>> print( matrix.shape )
(3, 3)
Matrix Operations : Matrix Reshaping
We can change the shape of matrix without changing the element of the Matrix by using reshape ().
>>> matrix = np.array( [ [ 4, 5, 6 ], [ 7, 8, 9 ], [ 10, 11, 12 ] ] )
>>> print ( matrix.reshape ( 1, 9 ) )
[[ 4 5 6 7 8 9 10 11 12]]
>>>
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Accessing the Elements of the Matrix with Python
Using following line of codes, we can access particular element, row or column of the matrix.
>>> import numpy as np
>>> matrix = np.array( [ [ 4, 5, 6 ], [ 7, 8, 9 ], [ 10, 11, 12 ] ] )
>>> print ( “2nd element of 1st row of the matrix = “, matrix [0] [1] )
2nd element of 1st row of the matrix = 5
>>> print ( ” 3d element of 2nd row of the matrix = “, matrix [1] [2] )
3d element of 2nd row of the matrix = 9
>>> print ( ” last element of the last row of the matrix = “, matrix [-1] [-1] )
last element of the last row of the matrix = 12
>>> print ( “Second row of the matrix = “, matrix [1] )
Second row of the matrix = [7 8 9]
>>> print ( “First row of the matrix = “, matrix [0] )
First row of the matrix = [4 5 6]
>>> print ( “Last row of the matrix = “, matrix [-1] )
Last row of the matrix = [10 11 12]
>>> print ( “Second column of the matrix = “, matrix [:, 1] )
Second column of the matrix = [ 5 8 11]
>>> print ( “First column of the matrix = “, matrix [:, 0] )
First column of the matrix = [ 4 7 10]
>>> print ( “Last column of the matrix = “, matrix [:, -1] )
Last column of the matrix = [ 6 9 12]
Addition of Matrices
Plus, operator (+) is used to add the elements of two matrices.
>>> import numpy as np
>>> X = np.array ( [ [ 8, 10 ], [ -5, 9 ] ] ) #X is a Matrix of size 2 by 2
>>> Y = np.array ( [ [ 2, 6 ], [ 7, 9 ] ] ) #Y is a Matrix of size 2 by 2
>>> Z = X + Y
>>> print (” Addition of Two Matrix : \n “, Z)
Addition of Two Matrix :
[[10 16]
[ 2 18]]
>>>
Multiplication of Matrices
Multiplication operator (*) is used to multiply the elements of two matrices.
>>> import numpy as np
>>> X = np.array ( [ [ 8, 10 ], [ -5, 9 ] ] ) #X is a Matrix of size 2 by 2
>>> Y = np.array ( [ [ 2, 6 ], [ 7, 9 ] ] ) #Y is a Matrix of size 2 by 2
>>> Z = X * Y
>>> print (” Multiplication of Two Matrix : \n “, Z)
Multiplication of Two Matrix :
[[ 16 60]
[-35 81]]
Subtraction of Matrices
Minus operator (-) is used to substract the elements of two matrices.
>>> import numpy as np
>>> X = np.array ( [ [ 8, 10 ], [ -5, 9 ] ] ) #X is a Matrix of size 2 by 2
>>> Y = np.array ( [ [ 2, 6 ], [ 7, 9 ] ] ) #Y is a Matrix of size 2 by 2
>>> Z = X – Y
>>> print ( ” Substraction of Two Matrix : \n “, Z)
Substraction of Two Matrix :
[[ 6 4]
[-12 0]]
>>>
Matrix Dot Products Calculation
The dot product of two matrix can perform with the following line of code.
>>> import numpy as np
>>> matrix1 = np.array( [ [ 4, 5, 6 ], [ 7, 8, 9 ], [ 10, 11, 12 ] ] )
>>> matrix2 = np.array( [ [ 1, 2, 1 ], [ 2, 1, 3 ], [ 1, 1, 2 ] ] )
>>> print ( ” The dot product of two matrix :\n”, np.dot ( matrix1 , matrix2 ) )
The dot product of two matrix :
[[20 19 31]
[32 31 49]
[44 43 67]]
>>>
Transpose of a Matrix
It is nothing but the interchange the rows and columns of a Matrix
>>> import numpy as np
>>> matrix = np.array ( [ [ 4, 5, 6 ], [ 7, 8, 9 ], [ 10, 11, 12 ] ] )
>>> print ( ” Matrix is : \n “, matrix)
Matrix is :
[[ 4 5 6]
[ 7 8 9]
[10 11 12]]
>>> print ( ” Transpose Matrix is : \n “, matrix.T )
Transpose Matrix is :
[[ 4 7 10]
[ 5 8 11]
[ 6 9 12]]
>>>
Accessing the Diagonal of a Matrix
Sometime we are only interested in diagonal element of the matrix, to access it we need to write following line of code.
>>> import numpy as np
>>> matrix = np.array ( [ [ 4, 5, 6 ], [ 7, 8, 9 ], [ 10, 11, 12 ] ] )
>>> print ( ” Matrix is : \n “, matrix)
Matrix is :
[[ 4 5 6]
[ 7 8 9]
[10 11 12]]
>>> print ( ” Diagonal of the matrix : \n “, matrix.diagonal ( ) )
Diagonal of the matrix :
[ 4 8 12]
>>>
Inverse of Matrix
The inverse of the matrix can perform with following line of code
>>> import numpy as np
>>> matrix = np.array ( [ [ 4, 5, 6 ], [ 7, 8, 9 ], [ 10, 11, 12 ] ] )
>>> print ( ” Matrix is : \n “, matrix)
Matrix is :
[[ 4 5 6]
[ 7 8 9]
[10 11 12]]
>>> print ( ” Inverse of the matrix : \n “, np.linalg.inv (matrix) )
Inverse of the matrix :
[[-9.38249922e+14 1.87649984e+15 -9.38249922e+14]
[ 1.87649984e+15 -3.75299969e+15 1.87649984e+15]
[-9.38249922e+14 1.87649984e+15 -9.38249922e+14]]
>>>
