1
$\begingroup$

"Positive definite matrix" is a standard term in mathematics, espeically linear algebra. Are there grammatical, linguistic, or historical reasons why it was not called "positively definite matrix"?

$\endgroup$
0
2
$\begingroup$

According to Miller's Earliest Known Uses positive definite, as applied to forms, appears first in Pierpont's Lectures On The Theory Of Functions Of Real Variables (1905). Pierpont uses the reversed expression for numbers, e.g. "For, if $p\neq q$, say $p > q$, then $p-q$ is a definite positive rational number; call it d". Here "definite" and "positive" are thought as two separate characterizations rather than "definite" adverbially modifying "positive". Later he makes it explicit with forms:

"A form... which has always one sign, except at the origin where it necessarily vanishes, is called definite... If the sign of a definite form is positive, it is called a positive definite form; if negative, it is a negative definite form.".

Apparently, he does not have in mind adverbial modifiers as in "positively definite" or "definitely positive".

$\endgroup$
1
  • 1
    $\begingroup$ The OED lists an even earlier one: 1904 Trans. Amer. Math. Soc. 5 464 It is well known that there is always one such invariant, a positive-definite Hermitian form. $\endgroup$ Dec 25 '19 at 19:00

Not the answer you're looking for? Browse other questions tagged or ask your own question.