HigherDimensional Arrays for Collections of Numbers
Twodimensional arrays can be thought of as describing tables of values, with rows and columns (like a block of cells in a spreadsheet), and even higherdimensional arrays can be thought of as describing a whole collection of tables.
Suppose you measure the fasting glucose on five subjects on each of three treatment days. You could think of your 15 measurements being laid out in a 5×3 table (five subjects by three days). If you want to represent this entire table with a single variable name like Gluc, you can use doubleindexing, with the first index specifying the subject (1 through 5) and the second index specifying the day of the measurement (1 through 3).
Under that system, Gluc_{3,2} or Gluc[3,2] indicates the fasting glucose for subject 3 on day 2. And Gluc_{i,j} or Gluc[i,j] indicates the fasting glucose for the i^{th} subject on the j^{th} day.
Special terms are sometimes used to refer to arrays with one or two dimensions:

A onedimensional array is sometimes called a vector. But this can be confusing, because the word vector is also used in mathematics, physics, and biology to refer to completely different things.

A twodimensional array is sometimes called a matrix (plural: matrices). But this term is usually reserved for twodimensional arrays of numbers that are going to be manipulated by a special set of mathematical rules called matrix algebra. Mathematical descriptions of multiple regression make extensive use of matrix algebra.