DETAINER (from detain, Lat. detinere), in law, the act of keeping a person against his will, or the wrongful keeping of a person's goods, or other real or personal property. A writ of detainer was a form for the beginning of a personal action against a person already lodged within the walls of a prison; it was superseded by the Judgment Act 1838.
DETERMINANT, in mathematics, a function which presents itself in the solution of a system of simple equations.
1. Considering the equations
| ax | + | by | + | cz | = | d, |
| a′x | + | b′y | + | c′z | = | d′, |
| a″x | + | b″y | + | c″z | = | d″, |
and proceeding to solve them by the so-called method of cross multiplication, we multiply the equations by factors selected in such a manner that upon adding the results the whole coefficient of y becomes = 0, and the whole coefficient of z becomes = 0; the factors in question are b′c″ - b″c′, b″c - bc″, bc′ - b′c (values which, as at once seen, have the desired property); we thus obtain an equation which contains on the left-hand side only a multiple of x, and on the right-hand side a constant term; the coefficient of x has the value
a(b′c″ - b″c′) + a′(b″c - bc″) + a″(bc′ - b′c),
and this function, represented in the form
| a, | b, | c | , | ||
| a′, | b′, | c′ | |||
| a″, | b″, | c″ |