Talk:Stochastic matrix

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how would you find the stable distribution for this regular stochastic matrix?

(.2.3) (.8.7)

[edit] Contradiction

Well, is it the rows or the columns that have to individually sum to 1? See also these edits. Melchoir 08:14, 28 December 2005 (UTC)

It's the columns. See Mathworld. Chris 21:21, 31 December 2005 (UTC)

Not true. A stochastic matrix can either be row stochastic (where the rows each sum to 1) or column stochastic (where the columns each sum to 1). With a row stochastic matrix, the probability vectors are row vectors, you left-multiply the matrix by the vector. With a column stochastic matrix, the vectors are column vectors, and you right-multiply the matrix by the vector. For example, for a Markov chain described by stochastic matrix A and probability vector at time k, you would write

if the matrix were column stochastic and were a column vector, and

if the matrix were row stochastic and were a row vector. Mateoee 18:41, 17 November 2006 (UTC)

[edit] Regular stochastic matrices

I suggest that the sentence (definition) `A stochastic matrix P is regular ...' is rewritten in a form that avoids any confusion between the regularity of stochastic matrices used in this article and the regularity (= invertibility) of matrices in general.

I removed the link to the Invertible Matrix article, which hopefully helps with the ambiguity. I'm not an expert on this at this point, but it's certainly clear that the definition of regular stochastic matricies used here has nothing to do with invertibility. It might be useful to use another term (I've seen the term "ergodic", for example, used to describe such stochastic matricies) to avoid any other confusion, but I'm not yet sufficiently up to speed on this to feel comfortable making the edit. Mateoee 17:50, 20 November 2006 (UTC)