A scalar is a single number. Scalars are usually written in italics with lowercase variable names.

A vector is an array of scalar numbers. We can identify each individual number by its index in that ordering. Typically, we give vectors lowercase names in bold typeface, such as $\mathbf{x}$.

A matrix is a $2$-dimensional (2D) array of numbers. This means that every element in the matrix is identified by two indices, commonly $i$ representing the row-index and $j$ representing the column-index.