Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter D.2, Problem 6E
Program Plan Intro

To prove that A1 and BABT is symmetric.

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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. #UsePython
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. The determinant of an n X n matrix can be used in solving systems of linear equations, as well as for other purposes. The determinant of A can be defined in terms of minors and cofactors. The minor of element aj is the determinant of the (n – 1) X (n – 1) matrix obtained from A by crossing out the elements in row i and column j; denote this minor by Mj. The cofactor of element aj, denoted by Cj. is defined by Cy = (-1y**Mg The determinant of A is computed by multiplying all the elements in some fixed row of A by their respective cofactors and summing the results. For example, if the first row is used, then the determi- nant of A is given by Σ (α(CI) k=1 Write a program that, when given n and the entries in an n Xn array A as input, computes the deter- minant of A. Use a recursive algorithm.
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