# linear independence

Published articles for linear independence.

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## When Greedy Algorithms are Perfect: the Matroid

DevFeed: [When Greedy Algorithms are Perfect: the Matroid](<https://devfeed.tech/articles/when-greedy-algorithms-are-perfect-the-matroid-40364.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/08/26/when-greedy-algorithms-are-perfect-the-matroid/>)

Published: 2014-08-26T09:00:02Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>), [graph theory](<https://devfeed.tech/topics/graph-theory.md>), [Graphs](<https://devfeed.tech/topics/graphs.md>), [math](<https://devfeed.tech/topics/math.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [graph-theory](<https://devfeed.tech/tags/graph-theory.md>), [graphs](<https://devfeed.tech/tags/graphs.md>), [greedy](<https://devfeed.tech/tags/greedy.md>), [greedy-algorithm](<https://devfeed.tech/tags/greedy-algorithm.md>), [kruskal-s-algorithm](<https://devfeed.tech/tags/kruskal-s-algorithm.md>), [linear-independence](<https://devfeed.tech/tags/linear-independence.md>), [matroids](<https://devfeed.tech/tags/matroids.md>), [minimum-spanning-trees](<https://devfeed.tech/tags/minimum-spanning-trees.md>), [trees](<https://devfeed.tech/tags/trees.md>), [vertex](<https://devfeed.tech/tags/vertex.md>)

### AI overview

This article explains when greedy algorithms are guaranteed to produce optimal solutions. It introduces matroids as the framework characterizing that guarantee and uses the minimum spanning tree problem as an example, with background on matroid history and connections to linear algebra and graph theory.

### Source excerpt

Greedy algorithms are by far one of the easiest and most well-understood algorithmic techniques. There is a wealth of variations, but at its core the greedy algorithm optimizes something using the natural rule, "pick what looks best" at any step. So a greedy routing algorithm would say to a routing problem: "You want to visit all these locations with minimum travel time? Let's start by going to the closest one. And from there to the next closest one.

## Linear Algebra--A Primer

DevFeed: [Linear Algebra--A Primer](<https://devfeed.tech/articles/linear-algebra-a-primer-40204.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/06/19/linear-algebra-a-primer/>)

Published: 2011-06-19T18:39:40Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Matrix](<https://devfeed.tech/topics/matrix-org.md>), [Graphs](<https://devfeed.tech/topics/graphs.md>)

Tags: [adjacency-matrix](<https://devfeed.tech/tags/adjacency-matrix.md>), [algebra](<https://devfeed.tech/tags/algebra.md>), [eigenvalues](<https://devfeed.tech/tags/eigenvalues.md>), [eigenvectors](<https://devfeed.tech/tags/eigenvectors.md>), [graph](<https://devfeed.tech/tags/graph.md>), [history](<https://devfeed.tech/tags/history.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [linear-independence](<https://devfeed.tech/tags/linear-independence.md>), [linear-maps](<https://devfeed.tech/tags/linear-maps.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [matrices](<https://devfeed.tech/tags/matrices.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [primer](<https://devfeed.tech/tags/primer.md>), [transformation](<https://devfeed.tech/tags/transformation.md>), [vector](<https://devfeed.tech/tags/vector.md>), [vector-spaces](<https://devfeed.tech/tags/vector-spaces.md>)

### AI overview

This primer introduces linear algebra through its historical origins in solving systems of linear equations. It explains determinants, matrices, vector algebra, and linear transformations, and shows how matrices can model graphs and compute path counts.

### Source excerpt

Story Time Linear algebra was founded around the same time as Calculus (think Leibniz, circa 1700) solely for the purpose of solving general systems of linear equations. The coefficients of a system were written in a grid form, with rows corresponding to equations and columns to the unknown variables. Using a computational tool called the determinant (an awkward, but computable formula involving only the coefficients of the equations in a system), researchers were able to solve these systems, opening a world of information about the positions of celestial bodies and large-scale measurements (of geodesic arcs) on the surface of the earth.