Vectors

## Description

The basic Sage command to enter the vector

(1)\begin{align} \mathbf v = \begin{pmatrix} 1 \\ 1/2 \\ 1/3 \\ 1/4 \end{pmatrix} \end{align}

is `v = vector(QQ, 4, [1, 1/2, 1/3, 1/4])`. `QQ` designates that the vector is over the rationals.

## Sage Cell

#### Code

```
v = vector(QQ, 4, [1, 1/2, 1/3, 1/4])
v
```

## Options

#### Option

The number of coordinates in the vector `v` can be calculated with the Sage command `v.degree()`.

#### Code

```
v = vector(QQ, 4, [1, 1/2, 1/3, 1/4])
v.degree()
```

#### Option

The parent field of the vector `v` is given by `vparent()`.

#### Code

```
v = vector(CC, 4, [1, 1/2, 1/3, 1/4])
v.parent()
```

#### Option

The Sage command `v[2]`, returns the third entry in the vector `v`. Sage counts array entries beginning with .

#### Code

```
v = vector(QQ, 4, [1, 1/2, 1/3, 1/4])
v[2]
```

#### Option

The command `zero_vector` generates the zero vector.

#### Code

```
z = zero_vector(QQ, 5)
z
```

## Tags

CC: math.la.i.vec.coord

Primary Tags: linear algebra, multivariable calculus

Secondary Tags: vectors

## Related Cells

None

## Attribute

Permalink: http://linear.ups.edu/html/section-RREF.html

Author: R. Beezer

Date: 24 Jul 2017 14:41

Submitted by: Tom Judson