Write a function ref_triangular which uses reflections to turn an m X n matrix M into...
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Write a function ref_triangular which uses reflections to turn an m X n matrix M into an upper triangular matrix. The output should be a list [Q,R] where is a product of reflections and R is upper triangular such that M == Q@R. At the start of the function, set R= M. copy(). On the i th step of a for loop, we should apply a reflection R, such that if the j th column is x = Mc., then R,x=y where R[0./ where y = I R[J-1.j] I 0 so we use a reflection with normal vector r=RE: J-R[0, J1-... - RJ-1./1 v = R[:.jl - y. We use this particular form for y so that at the jth step, we do not mess up the lower diagonal part we already created in previous steps. Write a function ref_triangular which uses reflections to turn an m X n matrix M into an upper triangular matrix. The output should be a list [Q,R] where is a product of reflections and R is upper triangular such that M == Q@R. At the start of the function, set R= M. copy(). On the i th step of a for loop, we should apply a reflection R, such that if the j th column is x = Mc., then R,x=y where R[0./ where y = I R[J-1.j] I 0 so we use a reflection with normal vector r=RE: J-R[0, J1-... - RJ-1./1 v = R[:.jl - y. We use this particular form for y so that at the jth step, we do not mess up the lower diagonal part we already created in previous steps.
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Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
Posted Date:
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