Definition, Betydelse & Anagram | Engelska ordet DETERMINANT

Definition av DETERMINANT

1. (matematik) determinant

Exempel på hur man kan använda DETERMINANT i en mening

• In particular, the determinant is nonzero if and only if the matrix is invertible and the corresponding linear map is an isomorphism.
• This is the same structure as in the modern English term "skyscraper"; the base-word here would be "scraper", and the determinant "sky".
• The determinant of the unitary matrix is on the unit circle while that of the hermitian matrix is real and positive and since in the case of a matrix from the special linear group the product of these two determinants must be 1, then each of them must be 1.
• An LU decomposition gives a quick method for solving a Toeplitz system, and also for computing the determinant.
• Furthermore, the lipid serves as a mediator of membrane associations or as a determinant for specific protein-protein interactions.
• However this last fact can be proved in an elementary way as follows: the eigenvalues of a real skew-symmetric matrix are purely imaginary (see below) and to every eigenvalue there corresponds the conjugate eigenvalue with the same multiplicity; therefore, as the determinant is the product of the eigenvalues, each one repeated according to its multiplicity, it follows at once that the determinant, if it is not 0, is a positive real number.
• The Jacobian determinant also appears when changing the variables in multiple integrals (see substitution rule for multiple variables).
• To make a 1NF relation a 2NF relation, remove the functionally dependent attributes in the partial dependencies of the first normal form relation, and place those partial dependency dependent attributes in a relation where their corresponding determinant attributes are an entire candidate key.
• Consequently, the multiplicative inverse of an invertible matrix can be found by dividing its adjugate by its determinant.
• However, in the case of a ring being commutative, the condition for a square matrix to be invertible is that its determinant is invertible in the ring, which in general is a stricter requirement than it being nonzero.
• An indirect isometry is an affine transformation with an orthogonal matrix that has a determinant of −1.
• Minors obtained by removing just one row and one column from square matrices (first minors) are required for calculating matrix cofactors, which are useful for computing both the determinant and inverse of square matrices.
• In multivariable calculus, this theorem can be generalized to any continuously differentiable, vector-valued function whose Jacobian determinant is nonzero at a point in its domain, giving a formula for the Jacobian matrix of the inverse.
• The choice of notation and the name of the function reflects the fact that the function is analogous to a derivative in calculus in the sense that it describes the rate of change of density of one measure with respect to another (the way the Jacobian determinant is used in multivariable integration).
• A frequent theme of Wells's work, as in his 1901 nonfiction book Anticipations, was the history of humans' mastery of power and energy through technological advance, seen as a determinant of human progress.
• In the physical theory of the quantum Hall effect, the Vandermonde determinant shows that the Laughlin wavefunction with filling factor 1 is equal to a Slater determinant.
• In mathematics, specifically linear algebra, the Cauchy–Binet formula, named after Augustin-Louis Cauchy and Jacques Philippe Marie Binet, is an identity for the determinant of the product of two rectangular matrices of transpose shapes (so that the product is well-defined and square).
• The resulting determinant bundle is responsible for the phenomenon of tensor densities, in the sense that for an orientable manifold it has a nonvanishing global section, and its tensor powers with any real exponent may be defined and used to 'twist' any vector bundle by tensor product.
• Note that the multiples of the identity act trivially on all flags, and so one can restrict attention to the special linear group SL(n,F) of matrices with determinant one, which is a semisimple algebraic group; the set of lower triangular matrices of determinant one is a Borel subgroup.
• The determinant of the changes taking place in the post-war years was the development of Emilia Plater Wool Industry Plant, which in its heyday employed about 2,500 employees.

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