endlichdimensionaler

"Endlichdimensionaler" is a term used in mathematics, particularly in the fields of linear algebra and vector spaces. It refers to a space or a set that has a finite number of dimensions. In other words, an endlichdimensionaler space is one where the number of basis vectors required to span the space is finite.

For example, the Euclidean space R^n, where n is a positive integer, is endlichdimensionaler because it can be spanned by n basis vectors. In contrast, an infinite-dimensional space, such as the space of all real-valued functions, requires an infinite number of basis vectors to span it.

The concept of endlichdimensionaler spaces is fundamental in many areas of mathematics and its applications. It is used in the study of linear transformations, eigenvalues, and eigenvectors, among other topics. In practical terms, endlichdimensionaler spaces are often used to model real-world phenomena that can be described by a finite number of parameters.

In summary, an endlichdimensionaler space is a mathematical space that can be spanned by a finite number of basis vectors. This concept is crucial in various areas of mathematics and its applications.