Crossword clues for determinant
Longman Dictionary of Contemporary English
The Collaborative International Dictionary
Determinant \De*ter"mi*nant\, a. [L. determinans, p. pr. of determinare: cf. F. d['e]terminant.] Serving to determine or limit; determinative.
Determinant \De*ter"mi*nant\, n.
That which serves to determine; that which causes determination.
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(Math.) The sum of a series of products of several numbers, these products being formed according to certain specified laws;
Note: thus, the determinant of the nine numbers a, b, c,a', b', c',a'', b'', c'', is a b' c'' - a b'' c' + a' b'' c] - a' b c'' + a'' b' c. The determinant is written by placing the numbers from which it is formed in a square between two vertical lines. The theory of determinants forms a very important branch of modern mathematics.
(Logic) A mark or attribute, attached to the subject or predicate, narrowing the extent of both, but rendering them more definite and precise.
--Abp. Thomson.
Douglas Harper's Etymology Dictionary
c.1600 (adj.); 1680s (n.), from Latin determinantem (nominative determinans), present participle of determinare (see determine).
Wiktionary
a. Serving to determine or limit; determinative. n. 1 A determine factor; an element that determines the nature of something 2 (context linear algebra English) The unique scalar function over square matrix which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value of 1 for the unit matrix. Abbreviation: det 3 (context biology English) A substance that causes a cell to adopt a particular fate.
WordNet
adj. having the power or quality of deciding; "the crucial experiment"; "cast the deciding vote"; "the determinative (or determinant) battle" [syn: crucial, deciding(a), determinative, determining(a)]
n. a determining or causal element or factor; "education is an important determinant of one's outlook on life" [syn: determiner, determinative, determining factor, causal factor]
a square matrix used to solve simultaneous equations
Wikipedia
In linear algebra, the determinant is a useful value that can be computed from the elements of a square matrix. The determinant of a matrix A is denoted det(A), det A, or |A|.
In the case of a 2 × 2 matrix, the specific formula for the determinant is simply the upper left element times the lower right element, minus the product of the other two elements. Similarly, suppose we have a 3 × 3 matrix A, and we want the specific formula for its determinant |A|:
$\begin{align}|A| = \begin{vmatrix} a & b & c\\d & e & f\\g & h & i \end{vmatrix} &= a\,\begin{vmatrix} e & f\\h & i \end{vmatrix} - b\,\begin{vmatrix} d & f\\g & i \end{vmatrix} + c\,\begin{vmatrix} d & e\\g & h \end{vmatrix}\\ &= aei+bfg+cdh-ceg-bdi-afh.\end{align}$Each determinant of a 2 × 2 matrix in this equation is called a " minor" of the matrix A. The same sort of procedure can be used to find the determinant of a 4 × 4 matrix, the determinant of a 5 × 5 matrix, and so forth.
Determinants occur throughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and the determinant can be used to solve those equations, although more efficient techniques are actually used, some of which are determinant-revealing and consist of computationally effective ways of computing the determinant itself. The use of determinants in calculus includes the Jacobian determinant in the change of variables rule for integrals of functions of several variables. Determinants are also used to define the characteristic polynomial of a matrix, which is essential for eigenvalue problems in linear algebra. In analytical geometry, determinants express the signed n-dimensional volumes of n-dimensional parallelepipeds. Sometimes, determinants are used merely as a compact notation for expressions that would otherwise be unwieldy to write down.
It can be proven that any matrix has a unique inverse if its determinant is nonzero. Various other theorems can be proved as well, including that the determinant of a product of matrices is always equal to the product of determinants; and, the determinant of a Hermitian matrix is always real.
Usage examples of "determinant".
But where the differentiation of the biosphere and the noosphere was not complete, the biospheric identities sucked these movements back out of the noosphere and into the bodily or biological determinants.
Mood-regulation expectancies as determinants of dysphoria in college students.
And, as I earlier mentioned, in the horticultural societies where women were a large portion of the productive work force, a type of egalitarian arrangement was indeed at work, but this was secured not by stable legal and noospheric determinants, but simply by biospheric contingencies.
Yet another school fastens on the universal Circuit as embracing all things and producing all by its motion and by the positions and mutual aspect of the planets and fixed stars in whose power of foretelling they find warrant for the belief that this Circuit is the universal determinant.
The state of the sensorium is a far more basic determinant of behavior than cultural patterns of reward and punishment because we receive these very reinforcements themselves through the media of the senses.
Stalin, whose historical determinants found themselves grounded in nature, sublimated under the name of Genius, that is, something irrational and inexpressible: here, depoliticization is evident, it fully reveals the presence of a myth.
And a smaller, more neotenous brain enhanced his synaptic firing speed -- a determinant of intelligence.
This is the driving force behind the regime and all of its policies and so is the principal determinant of nearly every other aspect of Iraqi policy and society.
But where the differentiation of the biosphere and the noosphere was not complete, the biospheric identities sucked these movements back out of the noosphere and into the bodily or biological determinants.
The biosphere and noosphere had not been differentiated in these societies, and thus the social determinants always reverted to biospheric selection in times of stress, defense, or turmoil.
But if there is a Rubicon anywhere near 750 cubic centimeters, while differences of the order of 100 or 200 cubic centimeters do not-at any rate to us-seem to be compelling determinants of intelligence, might not the apes be intelligent in some recognizably human sense?
Tallying Up the Costs These three variables are likely to be the principal determinants of both the length of the campaign and the number of casualties the United States would take.
You have yours for physics and mathematics, determinants and momentum and conserved vector currents.
Several terms in the Lower-Left are carried over from Up from Eden and Eye to eye: pleromatic (physical/material), uroboric (reptilian/brain stem), and typhonic (paleomammalian/limbic), although these are all used in a very general sense (both here and in Eden), to indicate worldviews where these elements, although by no means the sole determinant, loom large in its primary concerns, often defining its most general atmosphere (and sometimes its most scarce resource).
It had Fourier series, Bessel functions, determinants, elliptic functions -- all kinds of wonderful stuff that I didn't know anything about.