Short notation for a column vector where each element is the mean of each row of a given matrix I have a matrix $A$ defined as:
$$
A = 
\begin{bmatrix}
a_{1,1} & a_{1,2} & \ldots & a_{1,m} \\
a_{2,1} & a_{2,2} & \ldots & a_{1,m} \\
\vdots & \vdots & \ddots & a_{1,m} \\
a_{n,1} & a_{n,2} & \ldots & a_{n,m}
\end{bmatrix}
$$
I have also a column vector $b$ defined as:
$$
b =
\begin{bmatrix}
b_{1} \\
b_{2} \\
\vdots \\
b_{n} 
\end{bmatrix}
= \frac{1}{m} 
\begin{bmatrix}
a_{1,1} + a_{1,2} + \ldots + a_{1,m} \\
a_{2,1} + a_{2,2} + \ldots + a_{1,m} \\
\vdots \\
a_{n,1} + a_{n,2} + \ldots + a_{n,m}
\end{bmatrix}
= \frac{1}{m} 
\begin{bmatrix}
\sum_{i=1}^m a_{1,i} \\
\sum_{i=1}^m a_{2,i} \\
\vdots \\
\sum_{i=1}^m a_{n,i}
\end{bmatrix}
$$
My question is: there is a way to define $b$ without using the elements of $A$ (e.g. $a_{1,1}, a_{1,2}, \ldots, a_{n,m}$) but only performing some operations on directly on A?

I think
$$b = \dfrac{1}{m}\begin{bmatrix}
a_{1,1} & a_{1,2} & \ldots & a_{1,m} \\
a_{2,1} & a_{2,2} & \ldots & a_{1,m} \\
\vdots & \vdots & \ddots & a_{1,m} \\
a_{n,1} & a_{n,2} & \ldots & a_{n,m}
\end{bmatrix} \underbrace{\begin{bmatrix} 1\\1\\ \vdots \\ 1\\1\end{bmatrix}}_{m\times1}=\dfrac{1}{m}A\,\vec{1}$$
is the most compact way.
