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Jul 28, 20231 min read

A (finitely generated) vector space is said to have dimension equal to if it has any Hamel Basis with elements¹. We denote it .

Footnotes

And this is unambiguous, since All Hamel bases have the same number of elements (in a finitely generated vector space). ↩

021a MOC Linear Algebra
A linear transformation between spaces of equal dimension is injective iff it's surjective iff it's an isomorphism
All Hamel bases have the same number of elements (in a finitely generated vector space)
An endomorphism is injective iff it's surjective
Every vector space is isomorphic to the cartesian product of its field
Every vector space with same dimension are isomorphic to each other
Kernel-Image Theorem
Linear Transformation Rank

Nicholas Funari Voltani