Koeffizientenvektor

A Koeffizientenvektor, or coefficient vector in English, is a fundamental concept in linear algebra and various scientific fields. It is a vector where each element represents the coefficient of a corresponding variable or basis element in a linear combination or equation. Essentially, it's a compact way to represent the scalar multipliers of a set of terms.

For instance, in a polynomial equation like $3x^2 + 2x - 1$, the Koeffizientenvektor could be represented as $[3, 2, -1]$, assuming the basis is ordered as $x^2, x, 1$. Similarly, in a system of linear equations, each row of the coefficient matrix can be viewed as a Koeffizientenvektor for the variables in that specific equation.

Koeffizientenvektoren are crucial for operations such as dot products, vector addition, and matrix multiplication. They are used extensively in data analysis, machine learning algorithms (like linear regression), signal processing, and physics to describe the relationships and magnitudes of different components within a system. The dimensionality of the Koeffizientenvektor corresponds to the number of variables or basis elements being considered.

---