MIT
18 06 -
Lecture 23
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This guarantees that one of the eigenvalues is equal to one This eigenvalue has an eigenvector associated with it that is greater than or equal to one Lecture 23 Markov Matrices All entries are greater than zero Each column adds to one All other eigenvalues are less than one in magnitude The maximum eigenvalue is one Example A and the transpose of A have the same eigenvalues Recall u A u Projections expansions with orthonormal basis so the basis is Fourier series det A I 0 and det A I 0 are the same equation Note since the columns of A I add to zero A I is singular dependent columns because the rows are dependent since 1 1 1 is in the left null space and the eigenvector is in the null space
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