Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

SBurchette Group Title

Can one take the limit of a matrix as it is multiplied by itself infinite times? We are using a matrix to model how a population changes over a given period of time. Repeated multiplication of the matrix will show how the percentages change after each period of time transpires. The question was will the population stabilize. So I reasoned that if the limit of repeated multiplications of the matrix approached specific values, that the population would indeed stabilize.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. Jemurray3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, you can do that. Look up Markov Matrix.

    • 2 years ago
  2. SBurchette Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Example/ Matrix A represents how the population changes over a week. Matrix B represents the population. So\[\lim_{t \rightarrow \infty}(B)A^t\] Would represent the population after t numbers of weeks transpire. I took this limit numerically and the product matrix consistently approached particular values.

    • 2 years ago
  3. Jemurray3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I'll explain.... are you familiar with diagonalization of a matrix?

    • 2 years ago
  4. SBurchette Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Not entirely, I'm in a elementary linear algebra class. We have just been covering matrix operations.

    • 2 years ago
  5. Jemurray3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I see. I'm not quite sure how to explain it to you without referencing diagonalization or at least eigenvalues and eigenvectors, but you are correct in that if the rows and columns of the matrix add to 1 and all of the entries are positive, repeated multiplication by itself will approach a constant result

    • 2 years ago
  6. SBurchette Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok, I suppose the question more of an application than a presentation of theory. I do anticipate diving deeper into matrix theory =) Thanks for the assistance.

    • 2 years ago
  7. Jemurray3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    What you stumbled on is actually a very deep result in matrix theory, it's just that you're not quite prepared to appreciate it yet. You'll get there soon, though.

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.