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Exercise: An Application to Markov chains

  • Thread starter sshh
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If A 2x2, show that A^-1 = A^T if and only if :
http://www.mathhelpforum.com/math-help/attachments/f5/20406d1294835445-exercise-application-markov-chains-untitled.png [Broken]

[Hint: If a^2+b^2=1, then a=cosθ, b= sinθ for some θ. Use cos(θ-)=cosθcosϕ+sinθsinϕ]
 
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Answers and Replies

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If A 2x2, show that A^-1 = A^T if and only if :
http://www.mathhelpforum.com/math-help/attachments/f5/20406d1294835445-exercise-application-markov-chains-untitled.png [Broken]

[Hint: If a^2+b^2=1, then a=cosθ, b= sinθ for some θ. Use cos(θ-)=cosθcosϕ+sinθsinϕ]
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There is a term missing in your hint. It should read. "Use cos(θ-ϕ)=cosθcosϕ+sinθsinϕ]"
 
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