Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
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Chapter A.5, Problem 17P
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Let f ∈ C+ 2π with a zero of order 2p at z. Let r>p and m = n/r. Then there exists a constant c > 0 independent of n such that for all nsufficiently large, all eigenvalues of the preconditioned matrix C−1 n (Km,2r ∗ f)Tn(f) are larger than c.
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If there is a non-singular matrix P such as P-1AP=D , matrix A is called a diagonalizable matrix. A, n x n square matrix is diagonalizable if and only if matrix A has n linearly independent eigenvectors. In this case, the diagonal elements of the diagonal matrix D are the eigenvalues of the matrix A.
A=({{1, -1, -1}, {1, 3, 1}, {-3, 1, -1}}) :
1
-1
-1
1
3
1
-3
1
-1
a)Write a program that calculates the eigenvalues and eigenvectors of matrix A using NumPy.
b)Write the program that determines whether the D matrix is diagonal by calculating the D matrix, using NumPy.
Ps: Please also explain step by step with " # "
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Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
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