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Applied Linear Algebra
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If shape of matrix is 5x3, what will be the shape of U matrix in SVD decomposition?
5x5
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What are eigenvectors and eigenvalues? How to calculate it in Python?
Eigenvector changes by a scalar factor when linear transformation is applied to it. Eigenvalues are levels of scaling. vec,val=np.linalg.eig(M)
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Determine if matrix stochastic?
No
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What output will be shown?
18
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How to find LU decomposition in Python and what values are returned?
P,L,U=np.linalg.lu(A), where P-permutation matrix, L -lower, U -upper triangular matrices
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How you multiple elements by elements of two matrices in Python?
A*B
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What output will be?
[[25, 8], [ 1, 2]]
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Symmetric matrices have orthogonal...
Eigenvectors
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How to check if vectors are orthogonal?
Dot product is 0
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How to find determinant in Python? What is determinant of given matrix?
np.linalg.det(C), -24
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How to find norm of vector in Python?
np.linalg.norm()
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How to multiply two matrices in Python?
A@B, np.dot(A,B)
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How to create 4x4 identity matrix in Python?
np.eye(4)
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What function returns you inverse of the matrix?
np.linalg.inv()
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How to plot this figure?
plt.imshow(A)
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Add code to plot the figure.
plt.plot([0,2],[0,2],"r") plt.plot([0,-1],[0,3],"k")
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What is the output?
5x5 identity matrix
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What is rank of matrix?
The maximum number of linearly independent columns or rows.
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How to find the norm of the matrix using trace?
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