dekompozíció

Dekompozíció is the process of breaking a complex system or object into simpler parts that can be analyzed or used separately. The term is used in various disciplines, and its precise meaning depends on the context. In general, decomposition aims to reveal structure, reduce complexity, and enable modular analysis or processing.

In mathematics and related fields, dekompozíció refers to representing an object as a combination of simpler components. Examples include prime factorization of integers, direct sum decompositions of vector spaces, and matrix factorizations such as LU, QR, or singular value decomposition. Spectral decomposition expresses a linear operator in terms of its eigenvalues and eigenvectors. In computer science and data analysis, functional or problem decomposition breaks a task into subproblems or components that can be developed and tested independently. Time series analysis often uses decomposition to separate a signal into trend, seasonal, and irregular parts, facilitating interpretation and modeling.

In chemistry, dekompozíció (chemical decomposition) describes reactions in which a compound breaks down into two or more simpler substances, usually requiring energy input. In linguistics and cognitive science, decomposition refers to breaking down complex constructs—such as words into morphemes or ideas into component concepts—into more elementary units for study or processing.

Dekompozícia is a foundational concept across disciplines, enabling simplification, analysis, and reconstruction. Its effectiveness depends on the independence of components and the availability of well-defined representations; in some systems, interactions between parts may complicate or limit clean decomposition.