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In mathematics, the determinant is a scalar-valued function of the entries of a square matrix.The determinant of a matrix A is commonly denoted det(A), det A, or | A |.Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix.
The prepositions à (' to, at ') and de (' of, from ') form contracted forms with the masculine and plural articles le and les: au, du, aux, and des, respectively.. Like the, the French definite article is used with a noun referring to a specific item when both the speaker and the audience know what the item is.
wife wò 2SG. POSS âka that nà the ani wò âka nà wife 2SG.POSS that the ´that wife of yours´ There are also languages in which demonstratives and articles do not normally occur together, but must be placed on opposite sides of the noun. For instance, in Urak Lawoi, a language of Thailand, the demonstrative follows the noun: rumah house besal big itu that rumah besal itu house big that ...
In mathematics, a determinantal point process is a stochastic point process, the probability distribution of which is characterized as a determinant of some function. They are suited for modelling global negative correlations, and for efficient algorithms of sampling, marginalization, conditioning, and other inference tasks.
The action of the determinants on the blastomeres is one of the most important ones. During the segmentation, cytoplasmic determinants are distributed among the blastomeres, at different times depending on the species and on the type of determinant. Therefore, the daughter cells resulting from the first divisions are totipotent : they can ...
In algebra, the Leibniz formula, named in honor of Gottfried Leibniz, expresses the determinant of a square matrix in terms of permutations of the matrix elements. If A {\displaystyle A} is an n × n {\displaystyle n\times n} matrix, where a i j {\displaystyle a_{ij}} is the entry in the i {\displaystyle i} -th row and j {\displaystyle j} -th ...
The most popular of which for computing functional determinants is the zeta function regularization. [1] For instance, this allows for the computation of the determinant of the Laplace and Dirac operators on a Riemannian manifold, using the Minakshisundaram–Pleijel zeta function. Otherwise, it is also possible to consider the quotient of two ...
In terms of its expression as a determinant of a (2n − 1) × (2n − 1) matrix (the Sylvester matrix) divided by a n, the determinant is homogeneous of degree 2n − 1 in the entries, and dividing by a n makes the degree 2n − 2. The discriminant of a polynomial of degree n is homogeneous of degree n(n − 1) in the roots.