Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A situation or surrounding substance within which something else originates, develops, or is contained: "Freedom of expression is the matrix, the indispensable condition, of nearly every form of freedom” ( Benjamin N. Cardozo).
 n. The womb.
 n. Anatomy The formative cells or tissue of a fingernail, toenail, or tooth.
 n. Anatomy See ground substance.
 n. Geology The solid matter in which a fossil or crystal is embedded.
 n. Geology Groundmass.
 n. A mold or die.
 n. The principal metal in an alloy, as the iron in steel.
 n. A binding substance, as cement in concrete.
 n. Mathematics A rectangular array of numeric or algebraic quantities subject to mathematical operations.
 n. Something resembling such an array, as in the regular formation of elements into columns and rows.
 n. Computer Science The network of intersections between input and output leads in a computer, functioning as an encoder or a decoder.
 n. Printing A mold used in stereotyping and designed to receive positive impressions of type or illustrations from which metal plates can be cast. Also called mat2.
 n. Printing A metal plate used for casting typefaces.
 n. An electroplated impression of a phonograph record used to make duplicate records.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The womb.
 n. The material or tissue in which more specialized structures are embedded.
 n. An extracellular matrix, the material or tissue between the cells of animals or plants.
 n. Part of the mitochondrion.
 n. The medium in which bacteria are cultured.
 n. A rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and representing graphs in graph theory.
 n. A twodimensional array.
 n. A table of data.
 n. A geological matrix, the outer material of a rock consisting of larger grains embedded in a material consisting of smaller ones.
 n. The sediment surrounding and including the artifacts, features, and other materials at a site.
 n. The environment from which a given sample is taken.
from the GNU version of the Collaborative International Dictionary of English
 n. The womb.
 n. That which gives form or origin to anything.
 n. The cavity in which anything is formed, and which gives it shape; a die; a mold, as for the face of a type.
 n. The earthy or stony substance in which metallic ores or crystallized minerals are found; the gangue.
 n. The five simple colors, black, white, blue, red, and yellow, of which all the rest are composed.
 n. The lifeless portion of tissue, either animal or vegetable, situated between the cells; the intercellular substance.
 n. A rectangular arrangement of symbols in rows and columns. The symbols may express quantities or operations.
from The Century Dictionary and Cyclopedia
 n. The womb; the uterus.
 n. Hence That which incloses anything, or gives origin to anything, like a womb.
 n. In mathematics, a rectangular array of quantities, usually square: so called because considered as a mold or set of compartments into which a certain number of quantities can be put, the leaving of one of the spaces unoccupied being in effect to put zero there. :
 n. a matrix with p columns and q rows. The types of two matrices are said to be complementary when p—p = q + q.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. (mathematics) a rectangular array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules
 n. mold used in the production of phonograph records, type, or other relief surface
 n. the body substance in which tissue cells are embedded
 n. an enclosure within which something originates or develops (from the Latin for womb)
 n. the formative tissue at the base of a nail
 n. (geology) amass of finegrained rock in which fossils, crystals, or gems are embedded
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

According to the Oxford Dictionary, a matrix is a gridlike array of elements; a lattice.

They have got what they call a matrix display, where you choose any number of hotels and any number of flights.

In addition to its decentralized international sales staff, ONC plans to create what it calls "matrix teams" of employees focused on a particular foreign region, each with its own goals, profitandloss performance statements, and dedicated resources.

Instead, the UM researchers propose an alternative model, which they call the matrix quality model.

Google Squared, which delivers results in matrix form and allows them users to select and edit the fields along both axes of the spreadsheet.

Then in matrix form the metric looks like diag ( 1,1,1,1) as a bilinear form.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

If we have local coordinates defined, we can then represent the metric tensor in matrix form, where, for our fourdimensional spacetime, we will have a 4×4 matrix with elements gμν.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

The epoxy matrix is very durable and resists most common chemicals.

The matrix is labelled with the cliches downward on the left (rows) and across the top (columns).
For those of you bothering to watch POTUS tonight.  Moe_Lane’s blog  RedState

The double bull matrix is large, portable blind with 360 degree visability.
I am looking to purchase a larger hub style blind than my Cabelas Lighting Setup.
bilby commented on the word matrix
"This is a genuine ground floor opportunity to shape a front line field force operating in a matrix structure."
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July 6, 2008
oroboros commented on the word matrix
May tricks!
December 28, 2006