A matrix (plural matrices) is a group of mathematical objects in a rectangular arrangement, like the figure below.
With these matrices can be calculated in certain ways. For example, by adding or multiplying matrices.
This article gives an overview of the different types of matrices.

The dimensions of the matrix are called \(p\) and \(q\).

A \(p ยท q\) - Matrix has \(p\) rows and \(q\) columns.

The position of an element is indicated by a double index.
In the term \(a_{ij}\), \(i\) denotes the index of the line and \(j\) the index of the column.

Matrices of one column or row are called vectors. Matrices with one column are column vectors.
Likewise, matrices with one row are row vectors.

Matrices or vectors may be transpose. That means that the 1st row becomes the 1st column, the 2nd row the 2nd column, etc.
The symbol to indicate a transpose is usually a capital superscript \(T\).