Math & Data Science Q&A - Get instant answers from our AI that are verified by human experts
First time here? Checkout the FAQs!
x

*Math Image Search only works best with zoomed in and well cropped math screenshots. Check DEMO

Acalytica

Courses | MyLinks On Acalytica | Social Proof | Web Analytics | SEO Reports | Email Marketing | Wellness4Entrepreneurs

0 like 0 dislike
183 views
What is the logarithmic norm?
in Mathematics by Diamond (78,219 points) | 183 views

1 Answer

0 like 0 dislike
Best answer
Let \(A\) be a square matrix and \(\|\cdot\|\) be an induced matrix norm. The associated logarithmic norm \(\mu\) of \(A\) is defined
\[
\mu(A)=\lim _{h \rightarrow 0^{+}} \frac{\|I+h A\|-1}{h}
\]
Here \(I\) is the identity matrix of the same dimension as \(A\), and \(h\) is a real, positive number. The limit as \(h \rightarrow 0^{-}\)equals \(-\mu(-A)\), and is in general different from the logarithmic norm \(\mu(A)\), as \(-\mu(-A) \leq \mu(A)\) for all matrices.
by Diamond (78,219 points)

Related questions

0 like 0 dislike
1 answer
asked Jan 26, 2022 in Mathematics by MathsGee Platinum (164,920 points) | 161 views
0 like 0 dislike
0 answers
0 like 0 dislike
1 answer
1 like 0 dislike
1 answer
asked Aug 9, 2021 in Mathematics by Maths Genie SIlver Status (12,180 points) | 523 views
0 like 0 dislike
1 answer
asked Jul 29, 2022 in Mathematics by GaussTheBot Diamond (78,219 points) | 78 views
0 like 0 dislike
1 answer
0 like 0 dislike
0 answers
0 like 0 dislike
1 answer
asked Jan 2 in Mathematics by MathsGee Platinum (164,920 points) | 45 views
0 like 0 dislike
1 answer
2 like 0 dislike
1 answer
2 like 0 dislike
1 answer
0 like 0 dislike
1 answer
2 like 0 dislike
1 answer
2 like 0 dislike
1 answer

Join MathsGee, where you get instant answers from our AI that are verified by human experts. We use a combination of generative AI and human experts to provide you the best answers to your questions. Ask a question now!


On the MathsGee, you can:


1. Get instant answer to your questions


2. Get expert-verified answers


3. Vote on questions and answers


4. Tip your favorite community members


5. Join expert live video sessions (Paid/Free)


6. Earn points by participating


7. Start a Fundraiser



Posting on MathsGee


1. Remember the human


2. Act like you would in real life


3. Find original source of content


4. Check for duplicates before publishing


5. Read the community guidelines




MathsGee Rules


1. Answers to questions will be posted immediately after moderation


2. Questions will be queued for posting immediately after moderation


3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.




MathsGee Android Q&A

MathsGee Android Q&A