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determinant    音标拼音: [dɪt'ɚmənənt]
判定

判定

determinant
行列式

determinant
行列式

determinant
adj 1: having the power or quality of deciding; "the crucial
experiment"; "cast the deciding vote"; "the determinative
(or determinant) battle" [synonym: {deciding(a)},
{determinant}, {determinative}, {determining(a)}]
n 1: a determining or causal element or factor; "education is an
important determinant of one's outlook on life" [synonym:
{determinant}, {determiner}, {determinative}, {determining
factor}, {causal factor}]
2: the site on the surface of an antigen molecule to which an
antibody attaches itself [synonym: {antigenic determinant},
{determinant}, {epitope}]
3: a square matrix used to solve simultaneous equations

Determinant \De*ter"mi*nant\, a. [L. determinans, p. pr. of
determinare: cf. F. d['e]terminant.]
Serving to determine or limit; determinative.
[1913 Webster]


Determinant \De*ter"mi*nant\, n.
1. That which serves to determine; that which causes
determination.
[1913 Webster]

2. (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.
[1913 Webster]

3. (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.
[1913 Webster]

120 Moby Thesaurus words for "determinant":
Altmann theory, DNA, De Vries theory, Galtonian theory,
Mendelianism, Mendelism, RNA, Verworn theory, Weismann theory,
Weismannism, Wiesner theory, allele, allelomorph, antecedent,
antecedents, authority, base, basis, birth, border line, bordering,
borderline, bound, boundary, boundary condition, boundary line,
bounding, bourn, break boundary, breakoff point, call, causation,
cause, cause and effect, ceiling, character, chromatid, chromatin,
chromosome, circumscription, coastal, compass, confine, cutoff,
cutoff point, deadline, delimitation, determinative, determiner,
determining, diathesis, division line, element, end, endowment,
etiology, eugenics, extreme, extremity, factor, finish, floor,
fringing, frontier, gene, genesiology, genetic code, genetics,
ground, grounds, hedge, hereditability, heredity, heritability,
heritage, high-water mark, inborn capacity, influence,
inheritability, inheritance, interface, limbic, limen, liminal,
limit, limitation, limiting, limiting factor, line,
line of demarcation, littoral, low-water mark, lower limit, march,
marginal, mark, matrocliny, mete, occasion, patrocliny,
pharmacogenetics, principle, reason, recessive character,
replication, rimming, skirting, start, starting line,
starting point, stimulus, target date, term, terminal,
terminal date, terminus, threshold, time allotment, upper limit,
weight


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  • Determinant of a Matrix - Math is Fun
    The determinant helps us find the inverse of a matrix, tells us things about the matrix that are useful in systems of linear equations, calculus and more Calculating the Determinant First of all the matrix must be square (i e have the same number of rows as columns) Then it is just arithmetic For a 2×2 Matrix
  • 4. 1: Determinants- Definition - Mathematics LibreTexts
    Learn the definition of the determinant Learn some ways to eyeball a matrix with zero determinant, and how to compute determinants of upper- and lower-triangular matrices Learn the basic properties of the determinant, and how to apply them
  • Determinant -- from Wolfram MathWorld
    Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations As shown by Cramer's rule, a nonhomogeneous system of linear equations has a unique solution iff the determinant of the system's matrix is nonzero (i e , the matrix is nonsingular)
  • Determinants - Meaning, Definition | 3x3 Matrix, 4x4 Matrix - Cuemath
    Determinants are the scalar quantities obtained by the sum of products of the elements of a square matrix and their cofactors according to a prescribed rule They help to find the adjoint, inverse of a matrix Further to solve the linear equations through the matrix inversion method we need to apply this concept
  • Determinant | Meaning, Properties, Definition | Britannica
    determinant, in linear and multilinear algebra, a value, denoted det A, associated with a square matrix A of n rows and n columns Designating any element of the matrix by the symbol a r c (the subscript r identifies the row and c the column), the determinant is evaluated by finding the sum of n ! terms, each of which is the product of the
  • Determinant of Matrix with Solved Examples - GeeksforGeeks
    The determinant of a matrix is a scalar value that can be calculated for a square matrix (a matrix with the same number of rows and columns) It serves as a scaling factor that is used for the transformation of a matrix It is a single numerical value that plays a key role in various matrix operations, such as calculating the inverse of a matrix or solving systems of linear equations
  • Determinant of a Matrix – Explanation Examples - The Story of . . .
    In this lesson, we will look at the determinant, how to find the determinant, the formula for the determinant of $ 2 \times 2 $ and $ 3 \times 3 $ matrices, and examples to clarify our understanding of determinants
  • Determinant - Math. net
    The determinant of an n x n square matrix A, denoted |A| or det (A) is a value that can be calculated from a square matrix The determinant of a matrix has various applications in the field of mathematics including use with systems of linear equations, finding the inverse of a matrix, and calculus
  • Definition of Determinant of Matrix - BYJUS
    The determinant of a matrix is the scalar value or number calculated using a square matrix The square matrix could be 2×2, 3×3, 4×4, or any type, such as n × n, where the number of column and rows are equal





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