Show that the function from Rnxn to R given by ||A||max = max |aj| is not a norm by stating which of the 4 matrix norm conditions it fails to satisfy, and by demonstrating this fact via an example.
Show that the function from Rnxn to R given by ||A||max = max |aj| is not a norm by stating which of the 4 matrix norm conditions it fails to satisfy, and by demonstrating this fact via an example.
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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![**Question:**
Show that the function from \( \mathbb{R}^{n \times n} \) to \( \mathbb{R} \) given by
\[
\|A\|_{\text{max}} = \max_{i,j} |a_{ij}|
\]
is not a norm by stating which of the 4 matrix norm conditions it fails to satisfy, and by demonstrating this fact via an example.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed3eef2a-70e8-485e-b91d-563de65921b3%2Fd285a1e0-80bb-44a5-82e0-5a158ec1426b%2Fspaw4l_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Show that the function from \( \mathbb{R}^{n \times n} \) to \( \mathbb{R} \) given by
\[
\|A\|_{\text{max}} = \max_{i,j} |a_{ij}|
\]
is not a norm by stating which of the 4 matrix norm conditions it fails to satisfy, and by demonstrating this fact via an example.
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