matrix
- 1A rectangular arrangement of numbers or terms in rows and columns, used for such purposes as transforming coordinates, solving systems of linear equations, and representing graphs.
Multiplying a vector by a rotation matrix turns it through a fixed angle.
The whole system of equations can be written compactly as a single matrix equation.
UsageThe plural is usually matrices (also matrixes). Give the size as rows by columns: a 3 × 2 matrix.
Note
Its size is given as rows by columns, a 3 × 2 matrix, and two matrices can be multiplied only when the first has as many columns as the second has rows. A square matrix is the kind that has a determinant and may have an inverse.
Checked 2 Nov 2026 · 4 facts
- Matrix dimensions are stated as rows by columns; a 3 × 2 matrix has three rows and two columns. mjo.osborne.economics.utoronto.ca
- For the product AB, A must have as many columns as B has rows. textbooks.math.gatech.edu
- A determinant is defined for a square matrix. math.libretexts.org
- A square matrix may have an inverse. math.libretexts.org
- 2
- 3The substance or tissue that surrounds and holds more specialized structures within it.
Cartilage consists of a few cells scattered through a dense, rubbery matrix.
Tooth enamel forms within a protein matrix that later hardens with minerals.
Note
Biologists use the word for whatever the specialized parts sit in, such as the rubbery substance of cartilage around its scattered cells or the mineralized material of bone. It surrounds and supports the specialized parts, and a word in front usually says which medium is meant, as in bone matrix or the extracellular matrix.
Checked 31 Oct 2026 · 3 facts
- Cartilage has a rubbery intercellular matrix surrounding its cells. staffsites.sohag-univ.edu.eg
- Bone matrix contains organic material, principally collagen, as well as mineral. openstax.org
- The matrix surrounds embedded cells or structures and can itself provide structural support, as in bone. openstax.org
- 4The setting or set of circumstances within which something is formed, grows, or comes into being.
Medieval guilds were the matrix out of which the modern university emerged.
Her early years in the newsroom became the matrix of everything she later wrote.
UsageOften the matrix out of which something grew, or the matrix of something.
Similarcradle, crucible, seedbed
Note
The figure keeps the womb meaning in view: a matrix is what something grows inside and emerges from, so the word likes out of which, in which and of. Edward Carpenter, in Pagan and Christian Creeds (1920), calls ritual dancing "the matrix out of which the Drama sprang". A mere setting surrounds a thing; a matrix implies the thing came from it.
Checked 31 Oct 2026 · 2 facts
- Edward Carpenter wrote Pagan and Christian Creeds, first published in 1920. edwardcarpenter.net
- Carpenter describes ritual dancing with the exact quoted wording. gutenberg.org
- 5The binding material of a composite, such as the resin surrounding the glass fibers in fiberglass.
Carbon fibers are laid into an epoxy matrix and cured under heat and pressure.
Concrete is a composite too: the cement paste serves as the matrix around the sand and gravel.
Similarbinder
Note
A composite splits the work between two or more materials: fibers or particles carry the load, while the matrix surrounds them, holds them in position and passes the load from one to the next. Composites are often named by their matrix, as in metal matrix composite, and the matrix may be a polymer, a metal or a ceramic.
Checked 31 Oct 2026 · 6 facts
- A composite can combine two or more distinct materials. asminternational.org
- Fibers or particles provide load-bearing reinforcement. archive.nptel.ac.in
- The matrix holds reinforcement in position. archive.nptel.ac.in
- The matrix binds reinforcement and transfers load between fibers. unsw.edu.au
- Composites are classified and named by their matrix, including metal matrix composites. en.wikipedia.org
- The matrix may be a polymer, metal, or ceramic. asminternational.org
- 6A grid-like array of electronic components, especially one used for encoding, decoding, or storing information.
Early computers stored data in a core matrix of tiny magnetic rings threaded on wires.
Hand-wired matrix boards controlled the sequence of moves in some early industrial robots.
Note
The grid here is literal. Burroughs Corporation's Digital Computer Principles (1962) describes vertical and horizontal wires with a transistor at each intersection, so a signal on one row and one column picks out a single point. That is how a decoder turns a code into one output among many, and why the word usually comes named by its parts: diode matrix, core matrix, transistor matrix.
Checked 31 Oct 2026 · 2 facts
- Burroughs Corporation's Digital Computer Principles was first published in 1962. worldradiohistory.com
- A decoder can convert an input code into selection of one output among many. ti.com
- 7The finer rock or sediment in which larger grains, crystals, fossils, or buried remains are embedded.
Preparators spent months freeing the skeleton from its limestone matrix.
Garnets stand out as red specks in a dark matrix of mica and quartz.
Note
Geologists read a rock as things set in a background, and the matrix is the background: a conglomerate is pebbles held in a sandy matrix, and garnets sit as specks in a finer rock. In an ore the matrix is the worthless rock around the valuable mineral, which miners also call gangue.
Checked 31 Oct 2026 · 5 facts
- A rock's matrix is the finer material surrounding larger embedded grains or crystals. en.wikipedia.org
- Conglomerate can contain pebbles embedded in a sandy matrix. uwaterloo.ca
- Garnets can be embedded in a finer-grained rock matrix. pmc.ncbi.nlm.nih.gov
- The matrix surrounding an ore mineral can be gangue. en.wikipedia.org
- Gangue comprises the commercially worthless minerals associated with valuable minerals in ore. deq.mt.gov
- 8The dense, enzyme-rich fluid filling the space inside the inner membrane of a mitochondrion, the structure that produces a cell's energy.
Enzymes of the citric acid cycle are dissolved in the mitochondrial matrix.
Protons pumped out of the matrix flow back in to drive the making of ATP.
Note
Inside a mitochondrion the matrix is the space enclosed by the inner membrane, a dense fluid packed with enzymes where the citric acid cycle runs. The folded membrane around it holds the machinery that captures energy. The full phrase mitochondrial matrix is the safe choice, since matrix alone could mean the material between cells.
Checked 31 Oct 2026 · 6 facts
- The mitochondrial matrix is enclosed by the inner membrane. en.wikipedia.org
- The matrix is a dense, protein-rich fluid containing numerous enzymes. learning.medicine.wsu.edu
- The citric acid cycle takes place in the mitochondrial matrix. openstax.org
- The inner mitochondrial membrane forms folds. nature.com
- The inner membrane contains machinery for electron transport and ATP production. digitalhistology.org
- Extracellular matrix is material between cells. en.wikipedia.org
Less common meanings
- 9A simulated world produced by computers, in which people live and experience everything as real without realizing it is fake.
The novel's heroine slowly learns that her city, her friends, and even her memories are part of a matrix run by machines.
Rebels in the game try to wake the sleepers who still believe the Matrix is the real world.
UsageOften capitalized, with the: trapped in the Matrix.
Similarsimulation
Note
This meaning was popularized by the 1999 film The Matrix, which is why it is so often capitalized and takes the: people are trapped in the Matrix, or break out of it. Used loosely, it carries the idea out of fiction, to any setting where people play roles laid down for them without noticing.
Checked 3 Nov 2026 · 2 facts
- The Matrix was released in 1999. en.wikipedia.org
- The film The Matrix popularized this meaning of matrix. en.wiktionary.org
- 10A mold in which something is cast or shaped, such as one used to cast printing type.
The jeweler pressed soft wax into the matrix to copy the medallion's design.
Craftsmen kept matrices for each design so a damaged piece could be recast.
Note
The word is a distant twin of mother: it comes from Old French matrice or Latin mātrīx, a breeding animal or womb, both from māter, "mother". The mold keeps that picture as the place where a thing takes its shape, and the same idea of a containing, shaping space runs through the technical senses, from biology to printing.
Checked 31 Oct 2026 · 3 facts
- Matrix and mother share an Indo-European ancestor. en.wiktionary.org
- Matrix derives through Old French or Latin from māter, meaning mother; Latin mātrīx meant a breeding female animal or womb. en.wiktionary.org
- A printing matrix provides the mold in which a letter takes shape. en.wikipedia.org
- 11In printmaking, the inked plate or block that carries the image from which prints are taken.
An etcher bites the drawing into a copper matrix with acid before inking it.
Museums label prints by the kind of matrix used, whether woodblock, copperplate, or stone.
Similarplate
Note
Printmakers use it as the umbrella word for whatever carries the image, whether woodblock, copperplate or stone; printing form means the same. In most processes, the print comes out as a mirror image of the matrix, so any lettering on it has to run backward. Unlike the typecaster's mold, which shapes metal, this one carries ink.
Checked 31 Oct 2026 · 5 facts
- Printmaking matrices include woodblocks, copperplates and lithographic stones. hauserwirth.com
- This applies to most printing processes. In offset lithography, two transfers preserve the orientation of the original plate image. slam.org
- Lettering must be backward on a block when the printing process reverses its image. nga.gov
- A typecasting mould shapes molten metal. mmop.org.au
- A printmaking matrix carries ink for transfer to paper. victoriagal.org.uk
- 12The womb, the organ in which offspring develop before birth.
Note
English kept the Latin meaning, and it is now rare, with womb and uterus doing its everyday work. Thomas Browne uses it as a matter of course in Pseudodoxia Epidemica; when Vladimir Nabokov has the matrix "pegging away automatically" in Ada (1969), the rare word is part of the comedy. Outside such deliberate effects, womb is the word to use.
Checked 31 Oct 2026 · 4 facts
- English matrix preserves the Latin meaning ‘womb’. en.wiktionary.org
- Thomas Browne uses matrix to mean ‘womb’ in Pseudodoxia Epidemica. en.wiktionary.org
- Vladimir Nabokov’s Ada contains the exact words ‘pegging away automatically’ describing the matrix. en.wiktionary.org
- Ada was first published in 1969. openlibrary.org
- 13In chemical analysis, everything in a sample other than the substance being measured.
- 14The medium in which bacteria are grown in the laboratory.
- 15Used of a clause within which another, subordinate clause is embedded.
- 16In old dyeing practice, the five colors black, white, blue, red and yellow, once thought to be the basis of all other shades.
More uses
- matrix managementa way of organizing a company where people report to two managers
Practice
Can you tell the meanings of matrix apart? Answer 3 quick questions from this page, or write your own sentence and AI will check it.
Origin
Latin māter ("mother") is the root behind both Latin mātrīx ("dam, womb") and Old French matrice ("womb"), and one or the other gave Middle English matris, matrice, or matrix. Mother descends from the same Indo-European ancestor. The simulated-reality slang use was popularized by the 1999 science-fiction action film The Matrix.
Checked 1 Nov 2026 · 6 facts
- Latin māter means “mother” and ultimately underlies Latin mātrīx (“dam, womb”) and Old French matrice. en.wiktionary.org
- Old French matrice meant “womb”. anglo-norman.net
- Middle English had the forms matris, matrice, and matrix, derived from Latin or Old French. quod.lib.umich.edu
- Mother and Latin māter descend from the same Indo-European ancestor. en.wiktionary.org
- The Matrix is a science-fiction action film released in 1999. en.wikipedia.org
- The film popularized the simulated-reality slang sense of matrix. en.wiktionary.org