finite-dimensional (english) - meaning, definition, translation, pronunciation

Part of Speech

Adjective

Phonetic Transcription

/fɪˈnaɪt dɪˈmɛnʃənəl/

Meaning and Usage

The term "finite-dimensional" refers to a space (such as a vector space) that has a finite basis or dimension, which means there are a limited number of vectors that can span the entire space. This concept is widely used in mathematics, particularly in linear algebra and functional analysis.

Frequency of use: The term is commonly used in both written and spoken contexts, particularly within academic and technical discussions related to mathematics, physics, and engineering.

Example Sentences

1. Finite-dimensional vector spaces are fundamental in linear algebra.
   Los espacios vectoriales de dimensión finita son fundamentales en álgebra lineal.

2. Many theorems in functional analysis apply specifically to finite-dimensional cases.
   Muchos teoremas en análisis funcional se aplican específicamente a casos de dimensión finita.

3. The study of finite-dimensional manifolds is crucial for understanding more complex geometries.
   El estudio de las variedades de dimensión finita es crucial para entender geometrías más complejas.

Idiomatic Expressions

The term "finite-dimensional" may not appear frequently in idiomatic expressions, but it is significant in mathematical contexts where finite dimensions are discussed.

Example Sentences with Mathematical Idioms

1. The principle of linear combinations works beautifully in finite-dimensional spaces.
   El principio de combinaciones lineales funciona de manera hermosa en espacios de dimensión finita.

2. In its finite-dimensional representation, the problem becomes much simpler to solve.
   En su representación de dimensión finita, el problema se vuelve mucho más sencillo de resolver.

3. Transitioning from infinite-dimensional to finite-dimensional interpretations can change the outcome of the solution.
   La transición de interpretaciones de dimensión infinita a dimensiones finitas puede cambiar el resultado de la solución.

Etymology

The word "finite" comes from the Latin "finitus," meaning "limited" or "bounded," while "dimensional" originates from "dimension," which traces back to the Latin "dimensionem," meaning "measurement." The combination of these parts indicates a space measurable within finite limits.

Synonyms and Antonyms

Synonyms: limited-dimensional, bounded-dimensional
Antonyms: infinite-dimensional, unbounded-dimensional