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
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Dimension theorem for vector spaces (Wikipedia)
Introduction, main theoremQuote, Introduction, main theorem
Given a vector space V, any two bases have the same cardinality.
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