Random Vectors

## Description

We can produce random elements of a vector space with the `.random_element()` method. This is useful for generating elements of the span of several vectors. For example, if we consider the subspace of $\mathbf Q^3$ spanned by vectors $(2, 3, 5)$ and $(7, 11, 13)$, then we can use `random_element` to generate random vectors in the span.

## Sage Cell

#### Code

```
V = QQ^3
S = V.span([vector(QQ, [2, 3, 5]), vector(QQ, [7, 11, 13])])
vecs = [(i, S.random_element()) for i in range(10)]
vecs
```

## Options

none

## Tags

Primary Tags:

Secondary Tags:

A list of possible tags can be found at The WeBWorK Open Problem Library. For linear algebra tags see the Curated Courses Project.

## Related Cells

- Vectors in Sage. Vectors in Sage.
- Linear Combinations of Vector Building Linear Combinations in Sage.
- Vector Addition & Subtraction. Adding and subtracting vectors in Sage.
- Vector Spaces in Sage Vector Spaces in Sage.
- Bases of Vector Spaces Using Sage to find bases of vector spaces.
- Vector Spans Finding the span of a finite set of vectors.
- Testing Sets for Linear Independence Testing a subset of a vector space for linear independence.

## Attribute

Permalink:

Author:

Date: 10 Apr 2020 16:41

Submitted by: Zane Corbiere