Linalg and numpy - Exercises
Contents
Linalg and numpy - Exercises¶
In these exercises you will practice linear algebra in addition to the numpy library
Task 1) Some basic numpy operations¶
a) Check your numpy version and make sure the newest version is installed. You can use the following command:
np.__version__
'1.20.3'
The newest version per 18/8/21 should be version 1.21.0
b) Create a matrix fillesd with 1’s at each element. The matrix should be of shape 10x10, do not use numpy
c) Now do the same thing as in b), but use numpy this time. Bonus exercise: Measure the time difference between the two implementations in ecercise b) and c)
d1) First create an array of elements in an aranged order from 0 to 9, using np.arange.
d2) Then use np.reshape to resahpe the array into the following matrix:
d3) Next task is to create some conditional statement, making all elements that are larger than 5 to be set as 1, and all elements that are less than 5 is set to 0, elements equal to 5 is unchanged.
e) Create three random 1d arrays x, y and z of length 3. Use the numpy function vstack and hstack to stack the arrays both vertically and horizontally as a matrix.
f) Create a random array of size 10. Print the mean, standard deviation and the variance using numpy
Task 2) A bit of linear algebra¶
a) Create a random matrix of size 3x3, containing only integers. Find the eigenvalues and eigenvectors using numpy.
b) Is this matrix invertible? Compute the determinant
c) If the matrix is invertible, find the invertible matrix
d) Check if the following matrix is symmetric, real orthogonal, hermitian and unitary. Also find the norm of the matrix.
e) Find the LU decomposition of matrix A:
What are the matrices L and U? You can try using numpy or scipy.linalg