Matrix and array have a mathematical and computer science meaning, such as Charles described. They also have an everyday meaning. In everyday use, a “matrix” usually refers to a sort of chart with rows and columns. You can use the chart to look up some fact. For example, a train or bus schedule is a kind of matrix that has routes across the top and stations along the side, and in the boxes of the chart are the times that the train arrives at each station. Array has a broader meaning of collection or set. Examples: “The jewelry store had an array of watches on display.” “We have an array of options for solving this problem.”

(Well, this looks like a homework assignment, but I indulge...) An array is basically a collection of objects that are arranged in a certain way. One of the simplest is a 1-dimensional array, and this is called a vector. A = { 1, 2, 3, 4, ...} Here, each object is represented by an index, e.g., A[1]. But an array can have any number of dimensions, even though it may not be possible to easily represent them in a visual way. One of the more common arrays is the 2-dimensional array (or sometimes called a rectangular array). These have rows and columns for indexing. An example that everyone is familiar with is a multiplication table. Specifically speaking, a matrix is a table representation of a 2-dimensional array. Here is an example of a matrix : A = 1 2 3 4 2 3 4 1 3 4 1 2 4 1 2 3 It is a 4 X 4 matrix that can be indexed as A[x,y]. Here, A[1,1] = 1. In short, a matrix is a subset of arrays, having the feataure of a table representation of a 2-dimensional array.

Let's consider the concepts of "pair" and "fraction." A pair of numbers is simply two numbers. A fraction is a pair of numbers that is given a special meaning and set of operations for working with them. The fraction 13/16 is not the same thing as the pair of numbers (13, 16). Similarly, in computer science, an "array" is a rectangular arrangement of numbers, a more general case; and a "matrix" is an array with a special mathematical meaning. In computer science, an "array" is a general way of arranging data. A two-dimensional array often is visualized as a rectangular grid with values in rows and columns. A 3 x 5 array would contain 15 values. One of the things that makes it an "array" is that are provisions in the computer language for accessing values by specifying the row and column number. (There can also be one-dimensional arrays or arrays with three or more dimensions). A "matrix" is a two-dimensional array that is taken to represent and store the values in the mathematical structure called a "matrix." Matrices are part of the field of mathematics called linear algebra. Matrices often represent the coefficients of systems of linear equations. Matrices are useful in doing coordinate transformations in multidimensional space. For example, in a video game, the locations of objects in three dimensional space might be represented as three-dimensional vectors. In order to calculate where these objects should appear on the screen, taking into account the direction of view and perspective, a very convenient way to do the calculations is by means of matrix operations. If you wanted to store a chess position in a computer, you might assign values to each piece--pawn = 1, knight = 2, rook = 3, and so forth--and store the positions of the pieces as values in an 8 by 8 array. This would be a case of an array that was not being used as a matrix.