Consider the following matrix A and it's inverse A-¹, TO 2 0 0 1 A = 1 0 0 1 " || B||4,4 A-¹ = = Let the "entry-wise" 4-norm of a m × n matrix B (or vector) be defined as 1/4 0 1 -1 m n ΣΣ bij | i=1 j=1 0.5 0 0 0 0 1 a) By hand, calculate || A||4,4. b) By hand calculate the condition number of A using the "entry-wise" 4-norm. (1) (2) Note, this norm is similar to the Euclidean-norm covered in class, just replacing the 2 with a 4 in the power and the root.
Consider the following matrix A and it's inverse A-¹, TO 2 0 0 1 A = 1 0 0 1 " || B||4,4 A-¹ = = Let the "entry-wise" 4-norm of a m × n matrix B (or vector) be defined as 1/4 0 1 -1 m n ΣΣ bij | i=1 j=1 0.5 0 0 0 0 1 a) By hand, calculate || A||4,4. b) By hand calculate the condition number of A using the "entry-wise" 4-norm. (1) (2) Note, this norm is similar to the Euclidean-norm covered in class, just replacing the 2 with a 4 in the power and the root.
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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Transcribed Image Text:Consider the following matrix A and it's inverse A-¹,
Го 1 01
A = 200
1 1
2
A-¹
=
1
m
n
|||B||4,4 = |bj|4
ΣΣ
i=1 j=1
1
Let the "entry-wise" 4-norm of a m × n matrix B (or vector) be defined as
1/4
0.5
0
0
1
a) By hand, calculate || A||4,4.
b) By hand calculate the condition number of A using the "entry-wise" 4-norm.
(1)
(2)
Note, this norm is similar to the Euclidean-norm covered in class, just replacing the 2 with a 4 in the power and the
root.
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