In general, a matrix (plural matrices) is something that provides support or structure, especially in the sense of surrounding and/or shaping. It comes from the Latin word for "womb", which itself derived from the Latin word for "mother", which is mater.
In biology, the word is used for the material between animal or plant cells, or generally the material (or "tissue") in which more specialized structures are embedded, and also specifically for one part of the mitochondrion. It is also used for the "medium" in which bacteria are grown (or "cultured"), so a Petri dish of agar may be the matrix for culturing a sample swabbed from someone's sore throat.
In geology, if a rock consists of larger grains embedded in a material consisting of smaller ones, this surrounding material (or "substrate") is termed matrix. For example, in Africa diamonds are often mined from a matrix of claylike rock called "yellow ground."
In archaeology, the matrix is the sediment surrounding and including the artifacts, features, and other materials at an archaeological site.
In the kind of printing that involves setting type, a matrix (often called a "mat") is a mold for shaping the letters  the mats of all the letters to go on one page are assembled, and then hot metal is poured into that matrix to make the plate to go into the printing press to print the page.
The U.S. Congress, in enacting the Federal Rules of Evidence, used the term in that sense to define a "duplicate" of a document that can be used as evidence at trial in place of the original:
In mathematics, a matrix is a rectangular table of data. A matrix with m rows and n columns is said to be an mbyn matrix. For example,
<math> \begin{bmatrix} 1 & 2 & 3 \\ 1 & 2 & 6 \\ 4 & 9 & 2 \\ 6 & 1 & 5 \end{bmatrix} </math>
is a 4by3 matrix.
Matrices in the mathematical sense are useful to record data that depend on two categories, such as the sales in three branches of a store in each of the four quarters of a year, or to keep track of the coefficients of linear expressions such as linear transformations and systems of linear equations. The field of mathematics that studies matrices is called matrix theory, a branch of linear algebra. Closely related terms from computing are "twodimensional array" and "spreadsheet".
We can do addition, multiplication and many different operations on matrices. To learn more, see Matrix (mathematics).
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