Definition:Vectorial Matroid
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Definition
Let $V$ be a vector space.
Let $S$ be a finite subset of $V$.
Let $\struct{S, \mathscr I}$ be the matroid induced by linear independence in $V$ on $S$.
From Matroid Induced by Linear Independence in Vector Space is Matroid, $\struct{S, \mathscr I}$ is a matroid.
Then any matroid isomorphic to $\struct{S, \mathscr I}$ is called a vectorial matroid.
Also see
- Definition:Matroid Induced by Linear Independence (Vector Space)
- Matroid Induced by Linear Independence in Vector Space is Matroid
Sources
- 1976: Dominic Welsh: Matroid Theory ... (previous) ... (next) Chapter $1.$ $\S 3.$ Examples of Matroids