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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 23EQ
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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.
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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