1. A fundamental concept in linear algebra consisting of a set of vectors with defined operations of vector addition and scalar multiplication that satisfy specific axioms (closure, associativity, commutativity, distributivity, etc.)
In mathematics, vector spaces form the foundation for studying linear transformations and solving systems of linear equations.
Na matemática, os espaços vetoriais formam a base para estudar transformações lineares e resolver sistemas de equações lineares.
2. An abstract mathematical structure where elements (vectors) can be added together and multiplied by scalars from a field, typically the real or complex numbers.
The set of all real numbers ℝ² is an example of a two-dimensional vector space over the real numbers.
O conjunto de todos os números reais ℝ² é um exemplo de um espaço vetorial bidimensional sobre os números reais.
Vector spaces are fundamental to both Brazilian and American mathematics education, appearing extensively in university-level linear algebra courses. The term is identical across Portuguese-speaking regions and is part of the universal language of mathematics in academic settings. No colloquial or regional variations exist for this technical term.