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Lecture 13: Markov Chain (Example)

Lecture 13: Markov Chain (Example)

This video was recorded at Stanford Engineering Everywhere EE263 - Introduction to Linear Dynamical Systems. If I put a vector in front of all ones – that's a row vector multiplied by P – I get this row vector here. This is the matrix way of saying that the column sums of P are all one. So this also if you look at it – if you like, I could put a lambda in there and say lambda is one. This basically says that P – that the vector of all ones is a left eigenvector of P, associated with eigenvalue lambda equals one. It tells you in particular P has an eigenvalue of one. But if it has eigenvalue of one, it also has a right eigenvector associated with lambda equals one. ... See the whole transcript at Introduction to Linear Dynamical Systems - Lecture 13

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