Deciding Initial state vector as row or column

Question

I am new to Markov Chain and Initial State Vectors, I have seen 2 different examples , in 1st example initial state vector was a row, and in another the vector was a column , how to decide the selection of row/column ?

Thanks !

Answer 1

People use different conventions that's all. The very same evolution can be written using left-matrix nomenclature

$$ a_{n+1} = M a_n $$

or right-matrix nomenclature

$$ b_{n+1} = b_n K $$

here a are column vectors, b are row vectors, and the relationship between the above two forms can be written as

$$ b_n = a_n^T, \;\;\;\; \mathrm{and} \;\;\;\; K = M^T $$