Write a function rot_triangular which takes a rectangular matrix MER where m > n as its...
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Write a function rot_triangular which takes a rectangular matrix MER where m > n as its input and outputs a list [Q,R] where Q is a rotation matrix, and R is upper triangular, such that M == Q@R. Hint: to rotate an n -dimensional vector v in the x1, x_j plane in such a way that the component is changed, and the i component is made to be 8, theta should be equal to np.arctan (v[i]/v[j]) (np.arctan computes the arctangent). Use a double for loop so that in column of the matrix, you rotate so that thej th entry (that is the diagonal entry) is changed and the i th entry is made to be zero for all i>j. This should be done over all i for j<i<m so you should loop over all j in range(n) and all i in range(j+1,m). Make sure to use R = M. copy() to create a copy of the input matrix so that you only make changes to the copy. Note: we could easily extend this to the case of rectangular matrices Write a function rot_triangular which takes a rectangular matrix MER where m > n as its input and outputs a list [Q,R] where Q is a rotation matrix, and R is upper triangular, such that M == Q@R. Hint: to rotate an n -dimensional vector v in the x1, x_j plane in such a way that the component is changed, and the i component is made to be 8, theta should be equal to np.arctan (v[i]/v[j]) (np.arctan computes the arctangent). Use a double for loop so that in column of the matrix, you rotate so that thej th entry (that is the diagonal entry) is changed and the i th entry is made to be zero for all i>j. This should be done over all i for j<i<m so you should loop over all j in range(n) and all i in range(j+1,m). Make sure to use R = M. copy() to create a copy of the input matrix so that you only make changes to the copy. Note: we could easily extend this to the case of rectangular matrices
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Sure Heres a possible implementation of the rottriangular function import numpy as np def rottriangu... View the full answer
Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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