(I - Q)^-1: Explanation of formula for steps until absorption in a DTMC

A more in-depth explanation of the (I - Q)^-1 formula for determining the expected number of steps until absorption in a DTMC (Discrete-Time Markov Chain).

00:00 - Intro and context
02:39 - Definitions
04:36 - Transition matrices revisited
07:37 - Developing a formula for expected steps until absorption
17:11 - Summary and conclusion

Linked below are helpful online resources. The first two, marked with asterisks, are the most relevant. I recommend taking a look at the second link (the Columbia notes on this topic) as they give the best overall explanation.

* The paper I mentioned in the video (found in the answers to one of the below MathOverflow posts) which linked substochastic transition matrices to spectral radii less than 1 (see Corollary 2.6):
https://arxiv.org/pdf/1701.06951.pdf

* Non-rigorous notes on deriving the (I - Q)^-1 formula:
https://www.columbia.edu/~ww2040/IEOR...

Thread on why (I - Q)^-1 equals I + Q + Q^2 + ...
https://www.physicsforums.com/threads...

An explanation on the intuition behind eigenvalues and eigenvectors:
https://math.stackexchange.com/questi...

Why powers of matrices with spectral radii less than 1 converge to 0:
https://math.stackexchange.com/questi...

General info on the relationship between infinite matrix series and inverse matrices:
https://math.stackexchange.com/questi...

Matrix norm Wikipedia page:
https://en.m.wikipedia.org/wiki/Matri...

Neumann series Wikipedia page:
https://en.m.wikipedia.org/wiki/Neuma...

Another MathOverflow post on power series and matrix inverses:
https://math.stackexchange.com/questi...

Info on the relationship between substochastic matrices and spectral radius:
https://math.stackexchange.com/questi...