2.1 Basic notation

We use:

- calligraphic letters to indicate sets (e.g., ${\cal A}$),

- lower case boldface Roman or Greek letters to indicate vectors (e.g., ${\mathbf{a}}$, $\mbox{\boldmath {$\alpha$}}$),

- upper case boldface Roman letters to indicate matrices (e.g., ${\mathbf{A}}$),

- superscripts in parentheses or subscripts to indicate family of related entities (e.g., ${\cal A}^{(1)}$, ${\mathbf{A}}_{{\cal A}_1}$),

- square brackets to indicate vector and matrix elements (e.g., ${\mathbf{a}}[1]$, ${\mathbf{A}}[1,2]$),

- sets of indices within square brackets to indicate subvectors or submatrices (e.g., ${\mathbf{a}}[{\cal A}]$, ${\mathbf{A}}[{\cal A},{\cal B}]$),

- ${\mathit{RowSum}}(\cdot)$ to indicate the diagonal matrix whose entry in position $(r,r)$ is the sum of the entries on the $r^{\rm th}$ row of the argument (which can be a rectangular matrix),

- ${\mathit{Norm}}(\cdot)$ to indicate a matrix whose rows are normalized,

- ${\mathbf{0}}$ to indicate a row vector or a matrix of 0's of the appropriate dimensions,

- ${\mathbf{1}}$ to indicate a row vector of 1's, of the appropriate dimension,

- $\mbox{\boldmath {$\pi$}}$ to indicate the steady state or the stationary probability distribution of a stochastic process^2.1,

- $\P$ to indicate the probability transition matrix of a discrete time Markov chain (DTMC)^2.2 unless differently specified, and

- ${\mathbf{Q}}$ to indicate the infinitesimal generator matrix of a continuous time Markov chain (CTMC)^2.3.