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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def covariance_matrix(self):
 """ Constructs the covariance matrix of input data from the singular value decomposition. Note that this is different than a covariance matrix of residuals, which is what we want for calculating fit errors. Using SVD output to compute covariance matrix X=UΣV⊤ XX⊤XX⊤=(UΣV⊤)(UΣV⊤)⊤=(UΣV⊤)(VΣU⊤) V is an orthogonal matrix (V⊤V=I), covariance matrix of input data: XX⊤=UΣ2U⊤ Because the axes represent identity in the PCA coordinate system, the PCA major axes themselves represent an affine transformation matrix from PCA to Cartesian space """


    a = N.dot(self.U,self.sigma)
    cv = N.dot(a,a.T)
    # This yields the covariance matrix in Cartesian
    # coordinates
    return cv