matrices

$\underbrace{ \begin{bmatrix} 1/2 & 1/2 & 0 & 0 & \cdots & 0\\ 0 & 1/2 & 1/2 & 0 & \cdots & 0\\ 0 & 0 & 1/2 & 1/2 & \cdots & 0\\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots\\ 1/2 & 0 & 0 & 0 & \cdots & 1/2\\ \end{bmatrix}}_{\displaystyle n} \left.\vphantom{\begin{bmatrix} 1/2 & 1/2 & 0 & 0 & \cdots & 0\\ 0 & 1/2 & 1/2 & 0 & \cdots & 0\\ 0 & 0 & 1/2 & 1/2 & \cdots & 0\\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots\\ 1/2 & 0 & 0 & 0 & \cdots & 1/2\\ \end{bmatrix}}\right\}m$

$\underbrace{ \begin{matrix} r{\left\{\vphantom{\begin{bmatrix} 1/2 & 0 & 0 & 0 & \cdots & 1/2\\ \end{bmatrix}}\right.}\\ s{\left\{\vphantom{\begin{bmatrix} \vdots & \vdots & \vdots & \ddots & \vdots & \vdots\\ 1/2 & 0 & 0 & 0 & \cdots & 1/2\\ \end{bmatrix}}\right.} \end{matrix} \begin{bmatrix} 1/2 & 1/2 & 0 & 0 & \cdots & 0\\ 0 & 1/2 & 1/2 & 0 & \cdots & 0\\ 0 & 0 & 1/2 & 1/2 & \cdots & 0\\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots\\ 1/2 & 0 & 0 & 0 & \cdots & 1/2\\ \end{bmatrix}}_{\displaystyle n} \left.\vphantom{\begin{bmatrix} \vdots & \vdots & \vdots & \ddots & \vdots & \vdots\\ 1/2 & 0 & 0 & 0 & \cdots & 1/2\\ \end{bmatrix}}\right\}m \left.\vphantom{\begin{bmatrix} 1/2 & 1/2 & 0 & 0 & \cdots & 0\\ 0 & 1/2 & 1/2 & 0 & \cdots & 0\\ 0 & 0 & 1/2 & 1/2 & \cdots & 0\\ \end{bmatrix}}\right\}q$

$\begin{matrix} & \mathrm{data} & \mathrm{info} & \mathrm{retrieval} &\mathrm{brain} &\mathrm{lungs} &\\ \end{matrix}\\ \begin{matrix} \mathrm{CS\,docs}{\left\{\vphantom{\begin{bmatrix} 1 & 1 & 1 & 0 & 0\\ 2 & 2 & 2 & 0 & 0\\ 1 & 1 & 1 & 0 & 0\\ 5 & 5 & 5 & 0 & 0\\ \end{bmatrix}}\right.}\\ \mathrm{MD\,docs}{\left\{\vphantom{\begin{bmatrix} 0 & 0 & 0 & 2 & 2\\ 0 & 0 & 0 & 3 & 3\\ 0 & 0 & 0 & 1 & 1\\ \end{bmatrix}}\right.} \end{matrix} \begin{bmatrix} 1 & 1 & 1 & 0 & 0\\ 2 & 2 & 2 & 0 & 0\\ 1 & 1 & 1 & 0 & 0\\ 5 & 5 & 5 & 0 & 0\\ 0 & 0 & 0 & 2 & 2\\ 0 & 0 & 0 & 3 & 3\\ 0 & 0 & 0 & 1 & 1\\ \end{bmatrix} = \begin{bmatrix} 0.18 & 0\\ 0.36 & 0\\ 0.18 & 0\\ 0.90 & 0\\ 0 & 0.53\\ 0 & 0.80\\ 0 & 0.27\\ \end{bmatrix} \times \begin{bmatrix} 9.64 & 0\\ 0 & 5.29\\ \end{bmatrix} \times \begin{bmatrix} 0.58 & 0.58 & 0.58 & 0 & 0\\ 0 & 0 & 0 & 0.71& 0.71\\ \end{bmatrix}$

$\begin{array}{c} \begin{matrix} & & & & & & \textcolor[rgb]{0,0.46,0}{\mathrm{d}} & \textcolor[rgb]{0,0.46,0}{\mathrm{i}} & \textcolor[rgb]{0,0.46,0}{\mathrm{r}} &\textcolor[rgb]{0.895, 0.543, 0.26}{\mathrm{b}} &\textcolor[rgb]{0.895, 0.543, 0.26}{\mathrm{l}} &\\ \end{matrix}\\ \begin{matrix} \textcolor[rgb]{0,0.46,0}{\mathrm{CS\,docs}}{\left\{\vphantom{\begin{bmatrix} 1 & 1 & 1 & 0 & 0\\ 2 & 2 & 2 & 0 & 0\\ 1 & 1 & 1 & 0 & 0\\ 5 & 5 & 5 & 0 & 0\\ \end{bmatrix}}\right.}\\ \textcolor[rgb]{0.895, 0.543, 0.26}{\mathrm{MD\,docs}}{\left\{\vphantom{\begin{bmatrix} 0 & 0 & 0 & 2 & 2\\ 0 & 0 & 0 & 3 & 3\\ 0 & 0 & 0 & 1 & 1\\ \end{bmatrix}}\right.} \end{matrix} \begin{bmatrix} \textcolor[rgb]{0,0.46,0}{1} & \textcolor[rgb]{0,0.46,0}{1} & \textcolor[rgb]{0,0.46,0}{1} & 0 & 0\\ \textcolor[rgb]{0,0.46,0}{2} & \textcolor[rgb]{0,0.46,0}{2} & \textcolor[rgb]{0,0.46,0}{2} & 0 & 0\\ \textcolor[rgb]{0,0.46,0}{1} & \textcolor[rgb]{0,0.46,0}{1} & \textcolor[rgb]{0,0.46,0}{1} & 0 & 0\\ \textcolor[rgb]{0,0.46,0}{5} & \textcolor[rgb]{0,0.46,0}{5} & \textcolor[rgb]{0,0.46,0}{5} & 0 & 0\\ 0 & 0 & 0 & \textcolor[rgb]{0.895, 0.543, 0.26}{2} & \textcolor[rgb]{0.895, 0.543, 0.26}{2}\\ 0 & 0 & 0 & \textcolor[rgb]{0.895, 0.543, 0.26}{3} & \textcolor[rgb]{0.895, 0.543, 0.26}{3}\\ 0 & 0 & 0 & \textcolor[rgb]{0.895, 0.543, 0.26}{1} & \textcolor[rgb]{0.895, 0.543, 0.26}{1}\\ \end{bmatrix} \end{array} = \begin{bmatrix} \textcolor[rgb]{0,0.46,0}{0.18} & 0\\ \textcolor[rgb]{0,0.46,0}{0.36} & 0\\ \textcolor[rgb]{0,0.46,0}{0.18} & 0\\\textcolor[rgb]{0,0.46,0}{ 0.90} & 0\\ 0 & \textcolor[rgb]{0.895, 0.543, 0.26}{0.53}\\ 0 & \textcolor[rgb]{0.895, 0.543, 0.26}{0.80}\\ 0 & \textcolor[rgb]{0.895, 0.543, 0.26}{0.27}\\ \end{bmatrix} \times \begin{bmatrix} \textcolor[rgb]{0,0.46,0}{9.64} & 0\\ 0 & \textcolor[rgb]{0.895, 0.543, 0.26}{5.29}\\ \end{bmatrix} \times \begin{bmatrix} \textcolor[rgb]{0,0.46,0}{0.58} & \textcolor[rgb]{0,0.46,0}{0.58} & \textcolor[rgb]{0,0.46,0}{0.58} & 0 & 0\\ 0 & 0 & 0 & \textcolor[rgb]{0.895, 0.543, 0.26}{0.71}& \textcolor[rgb]{0.895, 0.543, 0.26}{0.71}\\ \end{bmatrix}$

$\begin{array}{c} \begin{matrix} \mu & \mathbf{\tau_1} & \tau_2 \end{matrix} \\ \begin{bmatrix} 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix} \end{array}$