numpy.linalg library is used calculates
the determinant of the input matrix, rank of the matrix, Eigenvalues and
Eigenvectors of the matrix
-
Determinant Calculation
np.linalg.det is used to find the determinant of 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 ( ” Determinant of the matrix : \n
“, np.linalg.det ( matrix ) )
Determinant of the
matrix :
3.197442310920453e-15
The rank of a matrix rows (columns) is the maximum
number of linearly independent rows (columns) of this matrix, that is count of
number of non-zero rows. np.linalg.rank
is used to find the rank of the 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 ( ” Rank of the matrix : \n “,
np.linalg.matrix_rank ( matrix ) )
Rank of the matrix :
Eigenvectors are widely used in Machine Learning image
processing. Eigenvectors are vectors that when that transformation is applied,
change only in scale (not direction). np.linalg.eig() is used to find the eigen
values and eigen vectors of the matrix.
>>> import numpy as
>>> matrix =
np.array ( [ [ 4, 5, 6 ], [ 7, 8, 9 ], [ 10, 11, 12 ] ] )
>>> print ( ”
Matrix is : \n “, matrix)
Matrix is :
5 6]
8 9]
[10 11 12]]
>>> eigenvalues ,
eigenvectors = np.linalg.eig ( matrix )
>>> print(” eigenvalues
are : \n”, eigenvalues )
eigenvalues are :
[ 2.47279221e+01 -7.27922061e-01 1.52670994e-15]
>>> print (”
eigenvectors are : \n”, eigenvectors )
eigenvectors are :
[[-0.35200306 -0.76057531 0.40824829]
[-0.55343002 -0.05691242 -0.81649658]
[-0.75485698
0.64675048 0.40824829]]
