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 28.3, Problem 1E
Program Plan Intro
To prove that every diagonal element of a symmetrical positive defined matrix is positive.
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Find the product of the product of the elements of a matrix and the other elements of a matrix with random integer elements of 4 x 2 each
Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.)
Sufficient Condition for Diagonalization
If an n xn matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable.
Find the eigenvalues. (Enter your answers as a comma-separated list.)
Is there a sufficient number to guarantee that the matrix is diagonalizable?
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O No
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Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.)
1 2 4
A =
0 1 0
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