The dimension theorem for vector spaces states that every basis of a given vector space has the same number of elements, whether that number is finite or infinite. This common count is what defines the dimension of the vector space. The result is foundational to linear algebra, since it guarantees that a vector space's dimension is a well-defined property rather than an artifact of which basis happens to be chosen.
Facts
Classification
Statement Form StatementGiven a vector space V, any two bases have the same cardinality. 1 Connections
Has Statement Form
In Branch
Source Dimension theorem for vector spaces (Wikipedia)
Sources
1. Dimension theorem for vector spaces (Wikipedia)
Introduction, main theorem
Given a vector space V, any two bases have the same cardinality.
In Group: Linear Algebra and Matrix Theory, Lead section
In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have
In Branch: Linear Algebra, Lead section
In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.