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What is the corresponding eigenvalue? Edit Insert Formats B I U A E E E ΕΣΥ ΑΗ Given a matrix M, a steady state vector v is a vector that satisfies Mv = v. Explain why your work above proves that stochastic matrices always have steady state vectors. A stochastic matrix is a matrix whose entries are nonnegative, and where the entries in any given column add to 1. Among other things, they are used for modeling internet traffic. Let M be a stochastic matrix. Explain why M and MT have the same eigenvalues. Suggestion: Since you're not actually trying to find the eigenvalues, consider the characteristic polynomial. Edit Insert ▾ Formats BIUA ▾ ΣΕ ΑΗ Find an eigenvector for MT. Suggestion: Remember the entries of the columns of M add to 1. This means the entries of each row of MT add to 1.

What is the corresponding eigenvalue? Edit Insert Formats B I U A E E E ΕΣΥ ΑΗ Given a matrix M, a steady state vector v is a vector that satisfies Mv = v. Explain why your work above proves that stochastic matrices always have steady state vectors. A stochastic matrix is a matrix whose entries are nonnegative, and where the entries in any given column add to 1. Among other things, they are used for modeling internet traffic. Let M be a stochastic matrix. Explain why M and MT have the same eigenvalues. Suggestion: Since you're not actually trying to find the eigenvalues, consider the characteristic polynomial. Edit Insert ▾ Formats BIUA ▾ ΣΕ ΑΗ Find an eigenvector for MT. Suggestion: Remember the entries of the columns of M add to 1. This means the entries of each row of MT add to 1.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 14EQ
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What is the corresponding eigenvalue? Edit Insert Formats B I U A E E E ΕΣΥ ΑΗ Given a matrix M, a steady state vector v is a vector that satisfies Mv = v. Explain why your work above proves that stochastic matrices always have steady state vectors.
Transcribed Image Text:What is the corresponding eigenvalue? Edit Insert Formats B I U A E E E ΕΣΥ ΑΗ Given a matrix M, a steady state vector v is a vector that satisfies Mv = v. Explain why your work above proves that stochastic matrices always have steady state vectors.
A stochastic matrix is a matrix whose entries are nonnegative, and where the entries in any given column add to 1. Among other things, they are used for modeling internet traffic. Let M be a stochastic matrix. Explain why M and MT have the same eigenvalues. Suggestion: Since you're not actually trying to find the eigenvalues, consider the characteristic polynomial. Edit Insert ▾ Formats BIUA ▾ ΣΕ ΑΗ Find an eigenvector for MT. Suggestion: Remember the entries of the columns of M add to 1. This means the entries of each row of MT add to 1.
Transcribed Image Text:A stochastic matrix is a matrix whose entries are nonnegative, and where the entries in any given column add to 1. Among other things, they are used for modeling internet traffic. Let M be a stochastic matrix. Explain why M and MT have the same eigenvalues. Suggestion: Since you're not actually trying to find the eigenvalues, consider the characteristic polynomial. Edit Insert ▾ Formats BIUA ▾ ΣΕ ΑΗ Find an eigenvector for MT. Suggestion: Remember the entries of the columns of M add to 1. This means the entries of each row of MT add to 1.
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