HMM notation

Below you can see HMM notation which at least for me looks simple and more or less is quite commonly used. Worth to mention that HMM model representation as λ = (A, B, π) is common, A and B distribution matrixes elements representation still sometimes wary. Moreover, states and observations representation wary too, but in notation bellow I chosen notation that I prefer.

N	number of states
T	number of observations
S = {s1, ..., si, ... , sN}	states, where i = 1...N
O = {o1, ..., ok, ... , oT}	observations, where k = 1...T
A = {a11, ..., aij, ... , aNN}	state transition probability distribution, where aij constructed as follows: i = 1...N, j = 1...N, i - represents start state, j - represents end state.
B = {b11, ... , bik, ... , bNT}	state emission probability distribution, where bik constructed as follows: i = 1...N, k = 1...T, i - represents state, k - represents observation.
Π = {π1, ..., πi, ..., πN}	initial state probability distribution, where i = 1...N
Ω = {ω1, ..., ωi, ..., ωN}	terminal state probability distribution, where i = 1...N
λ = (A, B, π)	HMM model

Below you can see visualised notation:

Diagram 1. HMM model example