environmental determinant - meaning and definition. What is environmental determinant
Diclib.com
ChatGPT AI Dictionary
Enter a word or phrase in any language 👆
Language:

Translation and analysis of words by ChatGPT artificial intelligence

On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:

  • how the word is used
  • frequency of use
  • it is used more often in oral or written speech
  • word translation options
  • usage examples (several phrases with translation)
  • etymology

What (who) is environmental determinant - definition

SUM OF SIGNED TERMS OF N FACTORS FROM N×N MATRIX WITH NO TWO FACTORS SHARING ROW OR COLUMN
Determinants; Determanent; Determenant; Matrix determinant; Determinant expansion by minors; Determinant theorem; Determinant (mathematics); Determinant of a matrix; Determinant identities; Determinant mathematics; Determinance
  • The area of the parallelogram is the absolute value of the determinant of the matrix formed by the vectors representing the parallelogram's sides.
  • The volume of this [[parallelepiped]] is the absolute value of the determinant of the matrix formed by the columns constructed from the vectors r1, r2, and r3.
  • [[Rule of Sarrus]]

determinant         
(determinants)
A determinant of something causes it to be of a particular kind or to happen in a particular way. (FORMAL)
N-COUNT: usu with supp
Determinant         
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It allows characterizing some properties of the matrix and the linear map represented by the matrix.
Determinant         
·adj Serving to determine or limit; determinative.
II. Determinant ·noun That which serves to determine; that which causes determination.
III. Determinant ·noun The sum of a series of products of several numbers, these products being formed according to certain specified laws.
IV. Determinant ·noun A mark or attribute, attached to the subject or predicate, narrowing the extent of both, but rendering them more definite and precise.

Wikipedia

Determinant

In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one). The determinant of a matrix A is denoted det(A), det A, or |A|.

The determinant of a 2 × 2 matrix is

| a b c d | = a d b c , {\displaystyle {\begin{vmatrix}a&b\\c&d\end{vmatrix}}=ad-bc,}

and the determinant of a 3 × 3 matrix is

| a b c d e f g h i | = a e i + b f g + c d h c e g b d i a f h . {\displaystyle {\begin{vmatrix}a&b&c\\d&e&f\\g&h&i\end{vmatrix}}=aei+bfg+cdh-ceg-bdi-afh.}

The determinant of an n × n matrix can be defined in several equivalent ways. Leibniz formula expresses the determinant as a sum of signed products of matrix entries such that each summand is the product of n different entries, and the number of these summands is n ! , {\displaystyle n!,} the factorial of n (the product of the n first positive integers). The Laplace expansion expresses the determinant of an n × n matrix as a linear combination of determinants of ( n 1 ) × ( n 1 ) {\displaystyle (n-1)\times (n-1)} submatrices. Gaussian elimination express the determinant as the product of the diagonal entries of a diagonal matrix that is obtained by a succession of elementary row operations.

Determinants can also be defined by some of their properties: the determinant is the unique function defined on the n × n matrices that has the four following properties. The determinant of the identity matrix is 1; the exchange of two rows (or of two columns) multiplies the determinant by −1; multiplying a row (or a column) by a number multiplies the determinant by this number; and adding to a row (or a column) a multiple of another row (or column) does not change the determinant.

Determinants occur throughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and determinants can be used to solve these equations (Cramer's rule), although other methods of solution are computationally much more efficient. Determinants are used for defining the characteristic polynomial of a matrix, whose roots are the eigenvalues. In geometry, the signed n-dimensional volume of a n-dimensional parallelepiped is expressed by a determinant. This is used in calculus with exterior differential forms and the Jacobian determinant, in particular for changes of variables in multiple integrals.