Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1-α B Show that every 2 x 2 stochastic matrix has at least one steady-state vector. Any such matrix can be written in the form P = a 1-B where and are constants between 0 and 1. (There are two linearly independent steady-state vectors if a=B=0. Otherwise, there is only one.) If P is a stochastic matrix, then a steady-state vector, or equilibrium vector, for P is a probability vector q such that Pq=q. Pq=1. Pq=0. Pq=P.

1-α B Show that every 2 x 2 stochastic matrix has at least one steady-state vector. Any such matrix can be written in the form P = a 1-B where and are constants between 0 and 1. (There are two linearly independent steady-state vectors if a=B=0. Otherwise, there is only one.) If P is a stochastic matrix, then a steady-state vector, or equilibrium vector, for P is a probability vector q such that Pq=q. Pq=1. Pq=0. Pq=P.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Show that every 2x2 stochastic matrix has at least one steady-state vector. Any such matrix can be written in the form P = 1-α B α 1-B where x and ẞ are constants between 0 and 1. (There are two linearly independent steady-state vectors if a = ß= 0. Otherwise, there is only one.) If P is a stochastic matrix, then a steady-state vector, or equilibrium vector, for P is a probability vector q such that Pq=q Pq=1. 8] Pq=0. Pq=P.
Transcribed Image Text:Show that every 2x2 stochastic matrix has at least one steady-state vector. Any such matrix can be written in the form P = 1-α B α 1-B where x and ẞ are constants between 0 and 1. (There are two linearly independent steady-state vectors if a = ß= 0. Otherwise, there is only one.) If P is a stochastic matrix, then a steady-state vector, or equilibrium vector, for P is a probability vector q such that Pq=q Pq=1. 8] Pq=0. Pq=P.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS