late 14c., matris, matrice, "uterus, womb," from Old French matrice "womb, uterus" and directly from Latin mātrix (genitive mātricis) "pregnant animal," in Late Latin "womb," also "source, origin," from māter (genitive mātris) "mother" (see mother (n.1)).
The many figurative and technical senses are from the notion of "that which encloses or gives origin to" something. The general sense of "place or medium where something is developed" is recorded by 1550s; meaning "mould in which something is cast or shaped" is by 1620s; sense of "embedding or enclosing mass" is by 1640s.
The mathematical sense of "a rectangular array of quantities (usually square)" is because it is considered as a set of components into which quantities can be set. The logical sense of "array of possible combinations of truth-values" is attested by 1914. As a verb, in television broadcasting, from 1951.
"short love poem," especially one suitable for music, also "part-song for three or more voices," 1580s, from Italian madrigale, which is of uncertain origin; probably from Venetian dialect madregal "simple, ingenuous," from Late Latin matricalis "invented, original," literally "of or from the womb," from matrix (genitive matricis) "womb" (see matrix).
1570s, "insert (a name) in a register or official list," especially "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 mātricula "public register," diminutive of mātrix (genitive mātricis) "list, roll," also "sources, womb" (see matrix).
The connection of senses in the Latin word seems to be via confusion of Greek mētra "womb" (from mētēr "mother;" see mother (n.1)) and an identical but different Greek word mētra meaning "register, lot" (see meter (n.2)). Evidently Latin mātrix was used to translate both, though it originally shared meaning with only one.
Intransitive sense of "to be entered as a member of a university or college, to become a member of a body or society" is by 1851. Also from late 16c. in English as "to adopt as a child; to naturalize," from the other sense of the Latin word, but these meanings now are obsolete. A list or register of persons belonging to an order, society, etc. was a matricula (1550s), from a diminutive of Latin mātrix. Related: Matriculated; matriculating.
1610s, "mold or matrix in which anything is cast or formed to a particular shape" (a sense now obsolete); see plasma. In biology, the meaning "living matter of a cell, protoplasm" is attested by 1864.
late 15c., "settled arrangement," also "income, property," from establish + -ment. Meaning "established church" is from 1731; Sense of "place of business" is from 1832. Meaning "social matrix of ruling people and institutions" is attested occasionally from 1923, consistently from 1955; Emerson also seems to have used it once in more or less that sense.
1530s, a kind of document in Scottish law, from French signature (16c.) or directly from Medieval Latin signatura "signature, a rescript," in classical Latin "the matrix of a seal," from signatus, past participle of signare "to mark with a stamp, sign" (see sign (v.)).
Meaning "one's own name written in one's own hand" is from 1570s, replacing sign-manual (early 15c.) in this sense. Musical sense of "signs placed it the beginning of a staff to indicate the key and rhythm" is from 1806. Meaning "a distinguishing mark of any kind" is from 1620s.
1825, "electrotype, stereotype," from French cliché, a technical word in printer's jargon for "stereotype block," noun use of past participle of clicher "to click" (18c.), supposedly echoic of the sound of a mold striking metal (compare native click).
Originally, a cast obtained by letting a matrix fall face downward upon a surface of molten metal on the point of cooling, called in English type-foundries 'dabbing.' [OED]
Figurative extension to "trite phrase, worn-out expression" is first attested 1888, via the notion of the metal plate from which a print or design could be reproduced endlessly without variety, paralleling the sense evolution of stereotype. But this sense was not common in English until the 1920s, when it was identified as a French idiom. Related: Cliched (1928).
"point or minute spot on a surface," Old English dott, once, "speck, head of a boil," perhaps related to Norwegian dot "lump, small knot," Dutch dot "knot, small bunch, wisp," Old High German tutta "nipple;" a word of uncertain etymology.
Known from a single source c. 1000; the word reappeared with modern meaning "mark" c. 1530; not common until 18c. Perhaps this is a different word imitative of "the mark of a mere touch with the pen" (Wedgwood). In music, the meaning "point indicating a note is to be lengthened by half" is by 1806. Morse telegraph sense is from 1838. On the dot "punctual" is 1909, in reference to a clock dial face. Dot-matrix in printing and screen display is attested by 1975.
"design stamped on wax," especially an impressed figure attached to a document as evidence of authenticity, c. 1200, sel, sele, from Old French seel, seal "seal on a letter" (Modern French sceau), from Vulgar Latin *sigellum (source of Italian suggello, Spanish sello; also Old Frisian and Middle High German sigel, German Siegel), from Latin sigillum "small picture, engraved figure, seal," diminutive of signum "identifying mark, sign" (see sign (n.)).
An earlier borrowing directly from Latin is represented by Old English insigel. The use for "engraved device of some hard material used for imprinting a seal" (technically a matrix) is by c. 1300. Extended senses are via the notion of a seal used to mark and close a document to insure its secrecy (c. 1300). The meaning "an identifying mark" is from mid-14c.; especially one confirming goods and measures as conforming to standard. The technical sense of "what prevents the escape of a gas or liquid" is by 1853.