Online Etymology Dictionary

matador (n.): man who kills the bull in a bullfight, 1670s, from Spanish matador, literally "killer," from matar "to kill or wound," probably from Arabic mata "he died," from Persian (see second element in checkmate). Fem. form is matadora.
match (n.1): "stick for striking fire," late 14c., macche, "wick of a candle or lamp," from Old French meiche "wick of a candle," from Vulgar Latin *micca/*miccia (cf. Catalan metxa, Spanish mecha, Italian miccia), probably ultimately from Latin myxa, from Greek myxa "lamp wick," originally "mucus," based on notion of wick dangling from the spout of a lamp like snot from a nostril, from PIE root *meug- "slimy, slippery" (see mucus). Modern spelling is from mid-15c.

Meaning "piece of cord or splinter of wood soaked in sulfur, used for lighting fires, lamps, candles, etc." is from 1530. First used 1831 for the modern type of wooden friction match, and competed with lucifer for much of 19c. as the name for this invention.
match (n.2): "one of a pair, an equal," Old English mæcca, "companion, mate, one of a pair, wife, husband, one suited to another, an equal," from gemæcca, from Proto-Germanic *gamakon "fitting well together" (cf. Old Saxon gimaco "fellow, equal," Old High German gimah "comfort, ease," Middle High German gemach "comfortable, quiet," German gemach "easy, leisurely"), from PIE root *mak-/*mag- "to fit" (see make (v.)). Middle English sense of "matching adversary, person able to contend with another" (c.1300) led to sporting meaning "contest," first attested 1540s.
match (v.): "to join one to another" (originally especially in marriage), late 14c., from match (n.1). Meaning "to place (one) in conflict with (another)" is from c.1400. That of "to pair with a view to fitness" is from 1520s; that of "to be equal to" is from 1590s. Related: Matched; matching.
match-girl (n.): 1765, from match (n.1) + girl. The tragic story of "The Little Match-Girl" (Danish title Den lille pige med svovlstikkerne) by H.C. Andersen was published first in 1845, translated into English by 1847.
match-head (n.): 1860, from match (n.1) + head (n.).
matchbook (n.): also match-book, in reference to a folder holding fire-starting devices, 1913, from match (n.1) + book (n.).
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 (cf. 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.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 (v.2): "checkmate," c.1300, from Old French mater "to checkmate, defeat, overcome," from mat "checkmated" (see checkmate (v.)).
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 + ism.
materialist (n.): 1660s and after in various philosophical and theological senses, on model of French matérialiste, from material (n.) + -ist. Also cf. 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 (cf. Old Frisian meth, Old High German mad, German Mahd "mowing, hay crop"), from PIE *me- "to cut down grass or grain with a sickle or scythe" (see mow).
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" (cf. 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, plural of mathematic (see -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;" cf. Old High German Mahthilda, from mahti "might, power" + hildi "battle," from Proto-Germanic *hildiz "battle," from PIE *kel- (1) "to strike, cut." The name also was late 19c. Australian slang for "a traveller'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.
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 (1).
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.