Lưu ý: Bản dịch của mục này hiện đang được kiểm tra chất lượng, vì vậy một số nội dung tạm thời chỉ hiển thị bằng tiếng Anh.
Mục từ này chưa được dịch sang ngôn ngữ của bạn, vì vậy nội dung gốc được hiển thị bên dưới.
vector space
This term is a technical designation used exclusively within linear algebra and functional analysis. It describes a rigorous mathematical environment where operations of addition and scalar multiplication are defined, providing the foundation for much of modern physics and engineering.
In a pedagogical context, it is often contrasted with a subspace, which is a vector space contained within a larger one. Because it is a compound noun referring to a specific mathematical entity, it is treated as a countable noun in academic discourse, allowing for the discussion of multiple distinct spaces with different dimensions or fields.
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Ví dụ
We need to define the vector space before we can find the basis.
Is this set of polynomials actually a vector space?
The professor explained how a subspace is also a vector space in its own right.
I wonder if this function space qualifies as a vector space.
Every finite dimensional vector space has a basis.
Let us consider a real vector space of dimension n.
The problem asks us to prove that the given set is a vector space.
Wait, does the zero vector have to be in the vector space?