Matrix
Let's stack each vector in the set \( \set{\va_1, \ldots, \va_m} \) such that \( \va_i \in \real^n, \forall i \) as shown below and refer to the entire box by the symbol \( \mA \), a matrix.
$$
\mA = \begin{bmatrix}
\va_{1,1} & \ldots & \va_{1,n} \\
\vdots & \ddots & \vdots \\
\va_{m,1} & \ldots & \va_{m,n} \\
\end{bmatrix}
$$
Here, \( \va_{i,j} \) represents the \( j \)-th element of the \( i \)-th vector.
This composite representation of multiple vectors is known as a matrix.
It is a 2-dimensional data type.
Each horizontal list of elements is known as a row of the matrix.
For example, the elements \( [\va_{1,1}, \va_{1,2}, \ldots, \va_{1,n}] \) form the first row of the matrix \( \mA \).
Similarly, each vertical list of elements is known as a column of the matrix.
For example, the elements \( [\va_{1,1}, \va_{2,1}, \ldots, \va_{m,1}] \) form the first column of the matrix \( \mA \).
Naturally, the diagonal, or the list of elements from the top left to the bottom right, are known as the diagonal of the matrix.
For example, the elements \( [\va_{1,1}, \va_{2,2}, \ldots, \va_{n,n}] \) form the diagonal of the matrix \( \mA \).