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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.
In vector calculus, the Jacobian matrix (/ dʒ ə ˈ k oʊ b i ə n /, [1] [2] [3] / dʒ ɪ-, j ɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.
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 ...
Rule of Sarrus: The determinant of the three columns on the left is the sum of the products along the down-right diagonals minus the sum of the products along the up-right diagonals.
If the determinant and inverse of A are already known, the formula provides a numerically cheap way to compute the determinant of A corrected by the matrix uv T.The computation is relatively cheap because the determinant of A + uv T does not have to be computed from scratch (which in general is expensive).
The determinant of a square Vandermonde matrix is called a Vandermonde polynomial or Vandermonde determinant.Its value is the polynomial = < ()which is non-zero if and only if all are distinct.
In mathematics, the Wronskian of n differentiable functions is the determinant formed with the functions and their derivatives up to order n – 1.It was introduced in 1812 by the Polish mathematician Józef Wroński, and is used in the study of differential equations, where it can sometimes show the linear independence of a set of solutions.
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 is an matrix, where is the entry in the -th row and -th column of , the formula is