composantes

Composantes is the plural form of composante in French. It designates the parts or elements that together constitute a whole. The term is used in mathematics, physics, statistics, and signal processing to describe how a complex object can be understood in terms of its constituent directions, factors, or frequencies.

In mathematics, the components of a vector are the scalars that express the vector with respect to a basis. If v is written as v = sum vi ei in a basis {ei}, the vi are the components of v along each basis vector. They are obtained by projecting v onto the basis vectors (often vi = v · ei in orthonormal bases). Changing the basis changes the components according to a linear transformation.

In physics and engineering, components describe the contributions of a quantity along predefined axes, such as the x-, y-, and z-components of a force or velocity. A vector decomposition expresses a physical quantity in terms of its orthogonal components, facilitating analysis of motion, forces, or fields.

In statistics, the phrase composantes principales refers to the principal components in principal component analysis (PCA), which are the directions of maximum variance in the data. The data are projected onto these components, producing a lower-dimensional representation that preserves as much information as possible.

In signal processing, a signal can be viewed as a sum of frequency components, obtained via Fourier or similar transforms. These components reveal the spectral content of the signal and are useful for filtering, compression, and analysis.

In chemistry and materials science, composantes may denote constituents of a mixture or alloy, each contributing to overall composition, mass fractions, or phase structure.