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Mathematics

Linear Independence and Spanning Sets in Vector Spaces

Quick fact

The smallest number of vectors needed to span a space is called its dimension—for example, you need exactly two independent vectors to cover a plane, and three to cover our familiar 3D space. Adding more vectors beyond that will either be redundant or force the space to become infinite-dimensional.

Why this is interesting

Imagine you have a set of arrows. Can you always reach every point in space by scaling and adding them together? And do you ever have more arrows than you actually need?

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Linear Independence and Spanning Sets in Vector Spaces

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