P is a markov chain matrix (row rums = 1). Consider Q as the transpose of P, with column sums = 1 instead of row rums = 1. Will Q also have 1 as an eigenvalue?
2026-03-26 12:37:06.1774528626
Will the transpose of a Markov Chain matrix have an eigenvalue of 1?
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Yes; in general every square matrix has the same eigenvalues as its transpose. One way to see this is to note that a matrix has the same determinant as its transpose, and then note that $(A-\lambda I)^T = A^T - \lambda I$.