---
tag: 6DHEKJPVBZ
kind: concept
name: Weighted matroid
sources:
  - wikipedia: en:9401560@r1297133503
    locator: Weighted matroid
    note: adopted
    mention: wikipedia://en/9401560
    sections: [Summary]
same_as:
  wikidata: Q7979897
  wikipedia: Weighted matroid
inventory: [DWP5WZECJK]
---

## Summary

In [[combinatorics|0JKW7W7XFR]], a branch of mathematics, a **weighted matroid** is a matroid endowed with a function that assigns a weight to each element. Formally, let $M = (E, I)$ be a matroid, where *E* is the set of elements and *I* is the family of independent set. A weighted matroid has a *weight function* $w : E \rightarrow \mathbb{R}^+$ for assigns a strictly positive weight to each element of $E$. We extend the function to subsets of $E$ by summation; $w(A)$ is the sum of $w(x)$ over $x$ in $A$.