Linearsüsteem

Linearsüsteem is a term used in mathematics and engineering to describe a system that exhibits linearity. A linear system is characterized by two fundamental properties: additivity and homogeneity. Additivity means that if input A produces output X and input B produces output Y, then the combined input A+B will produce the combined output X+Y. Homogeneity, also known as the scaling property, states that if input A produces output X, then scaling the input by a constant factor 'c' (i.e., cA) will scale the output by the same factor (i.e., cX).

These properties imply that the response of a linear system is directly proportional to the input, and the sum of responses to individual inputs equals the response to the sum of those inputs. This predictability makes linear systems easier to analyze and solve compared to non-linear systems. Examples of linear systems can be found in various fields, including electrical circuits, mechanical vibrations, and signal processing. In mathematics, a linear system of equations is a set of equations where each equation is linear, meaning variables are only raised to the power of one and are not multiplied together. Solving such systems often involves techniques like substitution, elimination, or matrix operations. The study of linear systems is a cornerstone of many scientific and engineering disciplines due to their fundamental nature and the power of analytical tools available for their investigation.