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compute the spectral noam of meteices A-[!.!] and B = conclude that replacing any entry of matrid hy spect kal nokm. in this regarol about the 3eno can Enerease its Conn you Say what FRobenius nonm

compute the spectral noam of meteices A-[!.!] and B = conclude that replacing any entry of matrid hy spect kal nokm. in this regarol about the 3eno can Enerease its Conn you Say what FRobenius nonm

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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compute the spectral nohm of metaices A and B = Conclude that replacing any entry of matrid By 3eno can Emerease its spect kal nokm in this regarol about the what Can you Say Faobenius nonm?
Transcribed Image Text:compute the spectral nohm of metaices A and B = Conclude that replacing any entry of matrid By 3eno can Emerease its spect kal nokm in this regarol about the what Can you Say Faobenius nonm?
Expert Solution
Step 1

Given:

                   A=11-11 and B=1101

To do:

  1. Compute the spectral norm of the given matrices.
  2. Conclude that by replacing any entry in a matrix will increase its spectral norm.
  3. Discuss what happens to 2. in the case of Frobenius norm.

Spectral norm:

Let A be an n×n matrix, then the spectral norm of A is

                                                                     A2=λmaxA*A

where A* is the conjugate transpose of A and λmaxA*A is the largest eigen value of A*A.

Frobenius norm:

et A be any m×n matrix, then the Frobenius norm of A is

                                                                     AF=∑i=1m∑j=1naij2

i.e., Frobenius norm of a matrix is the square root of the sum of the squares of the elements of the matrix.

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