koeficienti

Koeficienti is the plural form of the term koeficijent, used in several South Slavic languages such as Croatian, Serbian, and Bosnian. In mathematics and related fields, a koeficijent is a numerical factor that multiplies a variable, a term, or a function, and it can be real, complex, rational, or integral depending on the context.

In algebra and calculus, koeficienti appear as the constants that multiply variables or powers in expressions. For example, in the polynomial p(x) = 3x^2 + 2x + 1, the koeficienti are 3, 2, and 1. In a differential equation like dy/dx + by = c, the numbers a and b (when present with derivatives or terms) are koeficienti of the corresponding derivatives or terms. In linear algebra, koeficienti can form rows and columns of matrices that represent systems of equations or linear transformations.

Binomial coefficients, which count the ways to choose k elements from a set of n, are also referred to as koeficienti in some contexts. They appear as the coefficients in the expansion of (x + y)^n and are denoted by C(n, k) = n! / (k!(n − k)!). These combinatorial koeficienti are integers and can be depicted in Pascal’s triangle.

In statistics and applied sciences, koeficienti describe relationships or properties. Regression coefficients measure the expected change in a dependent variable per unit change in a predictor. The correlation coefficient assesses the strength of a linear relationship. Physical sciences use coefficients such as the coefficient of friction or the coefficient of thermal expansion to express material behavior.

Koeficienti are, in general, context-dependent constants that link variables, terms, or measurements within a model, equation, or representation.