A stochastic matrix is a matrix whose entries are nonnegative, and where the entries in any...
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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 B I U X, X’ Α' Α = = :三 =- € @ هي 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. Edit Insert Formats BI I U x₂ x² A A <> = = = :▼ GJ & Σ+ Σ Α What is the corresponding eigenvalue? Edit Insert Formats BIU X₂ X² = = = EVE E ② دی A Σ+ Σ ΑΗ ▼ A O Σ+ Σ Α 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 B I U X, X’ Α' Α = = :三 =- € @ هي 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. Edit Insert Formats BI I U x₂ x² A A <> = = = :▼ GJ & Σ+ Σ Α What is the corresponding eigenvalue? Edit Insert Formats BIU X₂ X² = = = EVE E ② دی A Σ+ Σ ΑΗ ▼ A O Σ+ Σ Α 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.
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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