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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 epidemiology, a risk factor or determinant is a variable associated with an increased risk of disease or infection. [ 1 ] : 38 Due to a lack of harmonization across disciplines, determinant , in its more widely accepted scientific meaning , is often used as a synonym.
Synonym for generalized permutation matrix. Moore matrix: A row consists of a, a q, a q², etc., and each row uses a different variable. Nonnegative matrix: A matrix with all nonnegative entries. Null-symmetric matrix A square matrix whose null space (or kernel) is equal to its transpose, N(A) = N(A T) or ker(A) = ker(A T). Synonym for kernel ...
A generalization of the determinant to arrays of dimension greater than 2. (Cayley 1860) complete A complete system of invariants is a set of generators for the ring of invariants. concomitant A relative invariant of GL(V) acting on the polynomials over S n (V)⊕V⊕V*. conjunctive See Sylvester (1853, Glossary p. 543–548) connex
The Jacobian determinant is sometimes simply referred to as "the Jacobian". The Jacobian determinant at a given point gives important information about the behavior of f near that point. For instance, the continuously differentiable function f is invertible near a point p ∈ R n if the Jacobian determinant at p is non-zero.
Pages in category "Determinants" The following 47 pages are in this category, out of 47 total. This list may not reflect recent changes. ...
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The determinant of the left hand side is the product of the determinants of the three matrices. Since the first and third matrix are triangular matrices with unit diagonal, their determinants are just 1. The determinant of the middle matrix is our desired value. The determinant of the right hand side is simply (1 + v T u). So we have the result: