Span of a vector set

линейна обвивка

The span of a set of vectors is the collection of all vectors which can be represented by some linear combination of the set.

In simple terms, if you choose absolutely any vector, anywhere in , you can get to that vector using a linear combination of and . And because of that, you can say specifically that and span . If a set of vectors spans a space, it means you can use a linear combination of those vectors to reach any vector in the space.

In the same way, we can get to any vector, anywhere in , using a linear combination of the basis vectors , and span , the entirety of three-dimensional space.

These facts are denoted by:

We cannot span with fewer than vectors.

Given any two linearly independent vectors, we can use them to define the entire real plane ()!