Vector Spaces

## Description

We can create vector spaces of a given dimension over a given set of numbers in Sage. We will create a 5 dimensional vector space over the rationals in our example cell.

## Sage Cell

#### Code

```
V = VectorSpace(QQ, 5)
V
```

## Options

none

## Tags

CC:

Primary Tags: Linear Algebra: Abstract vector spaces

Secondary Tags: Abstract vector spaces: Definition and properties

## Related Cells

- Vectors in Sage. Vectors in Sage.
- Linear Combinations of Vector Building Linear Combinations in Sage.
- Bases of Vector Spaces Using Sage to find bases of vector spaces.
- Random Elements of Vector Sets Using Sage to fetch random elements of vector spaces.
- Vector Spans Finding the span of a finite set of vectors.
- Vector Addition & Subtraction. Adding and subtracting vectors in Sage.
- Finding a Scalar Product Finding the scalar product of a scalar and vector.
- Dot Product of Two Vectors Finding the dot product of two vectors.
- Cross Product of Two Vectors Finding the cross product of two vectors.
- Norm of a Vector Finding the norm (length) of a vector.
- Angle Between Two Vectors Finding the angle between two vectors.
- Testing Sets for Linear Independence Testing a subset of a vector space for linear independence.

## Attribute

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Author: R. Beezer

Date: 01 Mar 2020 21:39

Submitted by: Zane Corbiere