Jacobian determinant

(noun)

the determinant of the Jacobian matrix

Related Terms

Examples of Jacobian determinant in the following topics:

  • Determinants of 2-by-2 Square Matrices

    • The determinant of a square matrix is computed by recursively performing the Laplace expansion to find the determinant of smaller matrices.
    • The use of determinants in calculus includes the Jacobian determinant in the change of variables rule for integrals of functions of several variables.
    • 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.
    • In linear algebra, the determinant is a value associated with a square matrix.

  • Double Integrals in Polar Coordinates

  • Triple Integrals in Spherical Coordinates

  • Transformation of Radiative Transfer

  • Linear Approximation

    • Linear approximations for vector functions of a vector variable are obtained in the same way, with the derivative at a point replaced by the Jacobian matrix.

  • Sex Determination

    • Mammalian sex is determined genetically by the presence of X and Y chromosomes .
    • Avian sex determination is dependent on the presence of Z and W chromosomes.
    • This is referred to as environmental sex determination or, more specifically, as temperature-dependent sex determination.
    • In birds, Z and W chromosomes determine sex, with females being the heterozygous sex.
    • Differentiate among the various ways animals determine the sex of offspring

  • Rate-Determining Steps

    • The rate of a multi-step reaction is determined by the slowest elementary step, which is known as the rate-determining step.
    • In kinetics, the rate of a reaction with several steps is determined by the slowest step, which is known as the rate-determining, or rate-limiting, step.
    • We can picture the rate-determining step to be like the narrowest point in an hourglass; it is the "bottleneck" point of the reaction that determines how quickly reactants can become products.
    • If the second or a later step is rate-determining, determining the rate law is slightly more complicated.
    • The rate-determining step is like the narrowest point in the hourglass; it is the "bottleneck" point of the reaction that determines how quickly reactants can become products.

  • Self-Determination and New States

  • Molecularity

    • If a chemical reaction proceeds by more than one step or stage, its overall velocity or rate is limited by the slowest step, the rate-determining step.
    • When we describe the mechanism of a chemical reaction, it is important to identify the rate-determining step and to determine its "molecularity".
    • The molecularity of a reaction is defined as the number of molecules or ions that participate in the rate determining step.
    • A mechanism in which two reacting species combine in the transition state of the rate-determining step is called bimolecular.

  • Characteristics of the Product

    • The unique characteristics of a product should be used as inputs in determining the product's marketing mix.
    • Characteristics of a product also help to determine the price of a product.
    • This can determine where a product may fall on the price index.
    • It is the combination of demand for a product and its price that help determine the marketing mix.
    • The characteristics of a product determine the target market and price of a product.