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Applied Linear Algebra

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    Review of python
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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 output will be shown?
    18
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  • How to multiply two matrices in Python?
    A@B, np.dot(A,B)
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  • How you multiple elements by elements of two matrices in Python?
    A*B
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  • How to create 4x4 identity matrix in Python?
    np.eye(4)
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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 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 to plot this figure?
    plt.imshow(A)
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  • What is the output?
    5x5 identity matrix
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  • What function returns you inverse of the matrix?
    np.linalg.inv()
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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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  • What output will be?
    [[25, 8], [ 1, 2]]
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  • How to check if vectors are orthogonal?
    Dot product is 0
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  • Determine if matrix stochastic?
    No
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  • Symmetric matrices have orthogonal...
    Eigenvectors
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  • How to find norm of vector in Python?
    np.linalg.norm()
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