What does the notation $[\boldsymbol{A} | \boldsymbol{B} ]$ mean (line through a matrix)?

Question

I have just stumbled upon the following lecture slide, in which $G$ refers to a $k \times n$ matrix with linearly independent rows:

What does the notation with the line going vertically down the center of the matrix denote?

Answer 1

It means you're gluing these matrices. As in $$[A\mid B] = \left(\begin{array}{ccc|ccc} a_{11} & \cdots & a_{1n} & b_{11} & \cdots & b_{1m} \\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ a_{p1} & \cdots & a_{pn} & b_{p1} & \cdots & b_{pm}\end{array} \right),$$where $A = (a_{ij}) \in {\rm Mat}(p\times n, \Bbb R)$ and $B = (b_{ij}) \in {\rm Mat}(p\times m, \Bbb R)$. You can write it like that in $\LaTeX$ using the array environment. And of course you can use any ring $R$ instead of the reals $\Bbb R$ for the entries of the augmented matrix.

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[A\mid B] = \left(\begin{array}{ccc|ccc} 
a_{11} & \cdots & a_{1n} &
 b_{11} & \cdots & b_{1m} \\ 
\vdots & \ddots & \vdots &
 \vdots & \ddots & \vdots \\ 
a_{p1} & \cdots & a_{pn} & 
b_{p1} & \cdots & b_{pm}
\end{array} \right)