koeffisienti

Koeffisienti is a numerical factor that multiplies a variable or a term in an expression, equation, or mathematical model. It indicates the size, scale, or strength of that term.

In polynomials, coefficients are the numbers attached to each monomial. For example, in the polynomial 3x^2 - 5x + 7, the coefficients are 3, -5, and 7. The coefficient of x^2 is 3, the coefficient of x is -5, and the constant term 7 can be viewed as the coefficient of x^0.

In systems of linear equations, the coefficients form the coefficient matrix. The entry aij is the coefficient of variable xj in equation i. The matrix organizes all coefficients to facilitate solving the system, for instance by elimination or matrix factorization.

In statistics, coefficients describe relationships in models. Regression coefficients quantify how a one-unit change in a predictor affects the outcome. The correlation coefficient measures the strength and direction of a linear relationship between two variables.

In chemistry, stoichiometric coefficients specify the relative amounts of reactants and products in a balanced chemical equation, reflecting conservation of mass.

In analysis and signal processing, many coefficients arise as part of series or transforms. Fourier coefficients define the contribution of each basis function in a Fourier series, while Taylor (or Maclaurin) coefficients determine the terms of a power series expansion.

Coefficients can be real or complex numbers and may be constants or functions of other variables. They are distinguished from exponents and from constant terms that do not multiply a variable. To determine coefficients, one typically matches terms, expands expressions, or solves a corresponding system of equations.