determinant

noun

1. A determining factor; an element that determines the nature of something.

   “1999, Noah P. Barsky, Stuart Bruchey (editor), Organizational Determinants of Budgetary Influence and Involvement, Taylor & Francis (Garland Publishing), page 4, Shields and Young (1993) argue that the budget participation literature "has not produced a coherent nor unified definition" of both the determinants and consequences of budget participation.”

   “The field of the social determinants of health is perhaps the most complex and challenging of all.”

   “The aim of this book has been to assess the determinants of capital punishment without taking a stand for or against the death penalty.”

2. A scalar that encodes certain characteristics of a given transformation matrix; the unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value 1 for the unit matrix; abbreviated as: det.

   “1966 [Allyn & Bacon], Howard Whitley Eves, Elementary Matrix Theory, 1980, Dover, Unabridged corrected republication, page 165, The determinant of a square matrix A_(n) is a function (actually a polynomial function) of the elements a_ij of A.”

   “1990, Assem S. Deif, Advanced Matrix Theory for Scientists and Engineers, Gordon and Breach Science Publishers (Abacus Press), 2nd Edition, page 18, Show that the determinant of a Hermitian matrix is real and that of a skew-Hermitian matrix is imaginary.”

   “Using this definition, we derive the basic properties of a determinant that are useful in its evaluation. In particular, it is shown how the calculation of a determinant can be reduced to the calculation of determinants of lower order.”

   “The following proposition shows a connection between negafibonacci numbers and the determinants of a family of tridiagonal matrices. […] Assuming that the determinant det(Gₖ) = f₋₍ₖ₊₁₎ for all k ≤ n, we aim to show that det(Gₙ₊₂) = f₋₍ₙ₊₃₎.”

3. A substance that causes a cell to adopt a particular fate.
4. Something that causes a nuclease to cut at a specified point

adj

1. Serving to determine or limit; determinative.