Online Etymology Dictionary

matchbox (n.): also match-box, 1786, from match (n.1) + box (n.).
matchcoat (n.): fur-skinned mantle worn by Native Americans, 1640s, originally matchco, probably a native word (compare Ojibwa majigoode "petticoat, woman's dress"), altered by influence of coat (n.).
matchless (adj.): "peerless," 1520s, from match (n.2) + -less. Related: Matchlessly; matchlessness.
matchlock (n.): 1690s, from match (n.1), in reference to the firing mechanism, + lock (n.1) in the firearm sense (1540s); probably so called for its resemblance to a door-latching device.
matchmaker (n.): also match-maker, "marriage-broker," 1630s, from match (n.2) + maker. Related: Match-making.
mate (n.1): "associate, fellow, comrade," mid-14c., also "companion" (late 14c.), from Middle Low German mate, gemate "one eating at the same table, messmate," from Proto-Germanic *ga-maton "having food (*matiz) together (*ga-)," which is etymologically identical with companion. Cognate with Danish and Swedish mat, German Maat "mate," Dutch maat, from German. Meaning "one of a wedded pair" is attested from 1540s. Used as a form of address by sailors, laborers, etc., since at least mid-15c. Meaning "officer on a merchant vessel is from late 15c.
mate (v.2): "checkmate," c. 1300, from Old French mater "to checkmate, defeat, overcome," from mat "checkmated" (see checkmate (v.)).
mate (v.1): c. 1500, "to equal, rival," 1590s as "to match, couple, marry, join in marriage," from mate (n.1). Also, of animals, "to pair for the purpose of breeding." Related: Mated; mating.
mate (n.2): in chess, "a condition of checkmate," c. 1300, mat, from Middle French mat, from Old French mater (see mate (v.2)).
mater-: comb. form meaning "mother," from Latin mater (see mother (n.)).
materia medica (n.): "substances used in medicine," Latin, literally "medical matter."
material (adj.): mid-14c., "real, ordinary; earthly, drawn from the material world;" a term in scholastic philosophy and theology, from Old French material, materiel (14c.) and directly from Late Latin materialis (adj.) "of or belonging to matter," from Latin materia "matter, stuff, wood, timber" (see matter). From late 14c. as "made of matter, having material existence; material, physical, substantial;" from late 15c. as "important, relevant."
material (n.): late 14c., "substance, matter from which a thing is made," from material (adj.).
materialism (n.): 1748, "philosophy that nothing exists except matter" (from French matérialisme); 1851 as "a way of life based entirely on consumer goods." From material (n.) + ism.
materialist (n.): 1660s and after in various philosophical and theological senses, on model of French matérialiste, from material (n.) + -ist. Also see materialism.
materialistic (adj.): 1829, from materialist + -ic. Related: Materialistically.
materiality (n.): 1520s, "that which is the matter of something," from Modern Latin materialitas, from materialis (see material (adj.)). From 1560s as "quality of being material;" 1640s as "quality of being important to matters at hand."
materialization (n.): 1822, noun of action from materialize.
materialize (v.): 1710, "represent as material," from material (adj.) + -ize. Meaning "appear in bodily form" is 1880, in spiritualism. Related: Materialized; materializing.
materially (adv.): late 14c., from material (adj.) + -ly (2).
materiel (n.): 1814, from French matériel "material," noun use of adj. matériel (see material (adj.)). A later borrowing of the same word that became material (n.).
maternal (adj.): late 15c., from Old French maternel (14c.), from Vulgar Latin *maternalis, from Latin maternus "maternal, of a mother," from mater "mother" (see mother (n.1)).
maternity (n.): 1610s, "quality or condition of being a mother," from French maternité "motherhood" (15c.), from Medieval Latin maternitatem (nominative maternitas) "motherhood," from Latin maternus (see maternal). Used from 1893 as a quasi-adjective in reference to garments designed for pregnant women.
matey (n.): 1833, diminutive of mate (n.) in its "male friend" sense + -y (3).
math (n.1): American English shortening of mathematics, 1890; the British preference, maths, is attested from 1911.
math (n.2): "a mowing," Old English mæð "mowing, cutting of grass," from Proto-Germanic *mediz (source also of Old Frisian meth, Old High German mad, German Mahd "mowing, hay crop"), from PIE *me- (4) "to cut grass" (see mow (v.)).
mathematic (n.): late 14c. as singular noun, replaced by early 17c. by mathematics, from Latin mathematica (plural), from Greek mathematike tekhne "mathematical science," feminine singular of mathematikos (adj.) "relating to mathematics, scientific, astronomical; disposed to learn," from mathema (genitive mathematos) "science, knowledge, mathematical knowledge; a lesson," literally "that which is learnt;" related to manthanein "to learn," from PIE root *mendh- "to learn" (source also of Greek menthere "to care," Lithuanian mandras "wide-awake," Old Church Slavonic madru "wise, sage," Gothic mundonsis "to look at," German munter "awake, lively"). As an adjective, 1540s, from French mathématique or directly from Latin mathematicus.
mathematical (adj.): early 15c., from Latin mathematicus (see mathematic) + -al (1). Related: Mathematically.
mathematician (n.): early 15c., from Middle French mathematicien, from mathematique, from Latin mathematicus (see mathematic).
mathematics (n.): 1580s; see mathematic + -ics. Originally denoting the mathematical sciences collectively, including geometry, astronomy, optics.
maths (n.): see math.
Matilda: fem. proper name, from French Mathilde, of Germanic origin, literally "mighty in battle;" compare Old High German Mahthilda, from mahti "might, power" + hildi "battle," from Proto-Germanic *hildiz "battle" (see Hilda). The name also was late 19c. Australian slang for "a traveler's bundle or swag," hence the expression waltzing Matilda "to travel on foot" (by 1889).
In my electorate nearly every man you meet who is not "waltzing Matilda" rides a bicycle. ["Parliamentary Debates," Australia, 1907]
The lyrics of the song of that name, sometimes called the unofficial Australian national anthem, are said to date to 1893.
matin (n.): see matins.
matinee (n.): "afternoon performance," 1848, from French matinée (musicale), from matinée "morning" (with a sense here of "daytime"), from matin "morning," from Old French matines (see matins). Originally as a French word in English; it lost its foreignness by late 19c. For suffix, compare journey.
matins (n.): canonical hour, mid-13c., from Old French matines (12c.), from Late Latin matutinas (nominative matutinæ) "morning prayers," originally matutinas vigilias "morning watches," from Latin matutinus "of or in the morning," associated with Matuta, Roman dawn goddess (see manana). The Old English word was uht-sang, from uhte "daybreak."
matri-: word-forming element meaning "mother," from comb. form of Latin mater (genitive matris) "mother" (see mother (n.1)).
matriarch (n.): "mother who heads a family or tribe," c. 1600, from matri- + -arch, abstracted from patriarch.
matriarchal (adj.): 1780 (in reference to bee colonies); see matriarch + -al (1); "patterned after patriarchy" [Barnhart]. Related: Matriarchally.
matriarchy (n.): formed in English 1881 from matriarch + -y (4).
matricide (n.): 1590s, "action of killing one's mother," from French matricide, from Latin matricida "mother-killer," and matricidium "mother-killing," from comb. form of mater "mother" (see mother (n.1)) + -cida "killer," and -cidium "a killing," from caedere "to slay" (see -cide). Meaning "one who kills his mother" is 1630s. Related: Matricidal (adj.). Old English had moðorslaga "matricide, mother-slayer."
matriculate (v.): 1570s, "to admit a student to a college by enrolling his name on the register," from Late Latin matriculatus, past participle of matriculare "to register," from Latin matricula "public register," diminutive of matrix (genitive matricis) "list, roll," also "sources, womb" (see matrix).

The connection of senses in the Latin word seems to be via confusion of Greek metra "womb" (from meter "mother;" see mother (n.1)) and an identical but different Greek word metra meaning "register, lot" (see meter (n.2)). Evidently Latin matrix was used to translate both, though it originally shared meaning with only one. Related: Matriculated; matriculating.
matriculation (n.): 1580s, noun of action from matriculate (v.).
matrifocal (adj.): 1952, a term from sociology, from matri- + focal.
matrilineal (adj.): "pertaining to or descended from the mother's side," 1897, from matri- + lineal. Related: Matrilineage; matrilineally.
matrilocal (adj.): 1897, from matri- + local.
matrimonial (adj.): mid-15c., from Middle French matrimonial (14c.) and directly from Late Latin matrimonialis, from Latin matrimonium (see matrimony). Earlier as a noun meaning "a marriage" (late 15c.). Related: Matrimonially.
matrimony (n.): c. 1300, from Old French matremoine "matrimony, marriage" and directly from Latin matrimonium "wedlock, marriage," from matrem (nominative mater) "mother" (see mother (n.1)) + -monium, suffix signifying "action, state, condition."
matrix (n.): late 14c., "uterus, womb," from Old French matrice "womb, uterus," from Latin matrix (genitive matricis) "pregnant animal," in Late Latin "womb," also "source, origin," from mater (genitive matris) "mother" (see mother (n.1)). Sense of "place or medium where something is developed" is first recorded 1550s; sense of "embedding or enclosing mass" first recorded 1640s. Logical sense of "array of possible combinations of truth-values" is attested from 1914. As a verb from 1951.
matroclinous (adj.): "resembling the mother rather than the father," 1911, from matri- + Greek klinein "to lean" (see lean (v.)).
matron (n.): late 14c., "married woman" (usually one of rank), from Old French matrone "married woman; elderly lady; patroness; midwife," and directly from Latin matrona "married woman, wife, matron," from mater (genitive matris) "mother" (see mother (n.1)). Sense of "female manager of a school, hospital, etc." first recorded 1550s.