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.1, Problem 1E
Program Plan Intro
To prove that A+B and A-B are symmetric matrix.
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Students have asked these similar questions
subject : analysis of algorithm
Q.No.1: Consider the following chain of matrices having matrices A, B, C and D. You have to consider the digits of your Registration Number in the order of the matrix as given. Add 2 to the digit if its zero.
For example, your Reg_No. 19-Arid-797 has last digit 7, 2nd last digit 9 and 3rd last digit 7.
A B C
2 X last digit last digit X 2nd last digit 2nd last digit X 3nd last digit
D
3rd Last digit X 4
What will be the minimum number of multiplication to multiply these matrices? Show the order of multiplication as well.
Consider the following.
0 1
-3
A =
0 4
0 4
1 2
2 2
-1
2
(a) Verify that A is diagonalizable by computing P-AP.
p-1AP =
(b) Use the result of part (a) and the theorem below to find the eigenvalues of A.
Similar Matrices Have the Same Eigenvalues
If A and B are similar n x n matrices, then they have the same eigenvalues.
If A and B are rectangular matrices as the following:
A = (ay)pxq and B = (by)nxm and AB = BA, then
n=q=m=p
(q=n) and (mp)
m=p
q=n
(q=m) and (n = p)
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