﻿ √ – Algosim documentation
Algosim documentation: √

# √ (square root)

The square root operator.

## Syntax

• `√x`

• `x` is a number or a matrix

## Description

• For a non-negative real number `x`, `√x` is the unique non-negative real number whose square is `x`.

• For a complex number `z`, `√z` is the square root of `z` given by `z^(1/2) = exp(½ ln(z))`. This definition is also used for negative real numbers.

• For a positive semidefinite square matrix `A`, `√A` is the unique positive semidefinite matrix whose square is `A`.

• `√` is not defined for matrices that are not square and positive semidefinite.

## Notes

The prefix operator `√` is mapped to the `sqrt` function.

## Examples

`√50`
`7.07106781187	(=5⋅√2)`
`√−4`
`2⋅i`
`√i`
`0.707106781187 + 0.707106781187⋅i`
`√❨❨6, 1, 2❩, ❨1, 1, 2❩, ❨2, 2, 9❩❩`
```⎛2.41100672391  0.254228867907 0.349877492821⎞
⎜0.254228867907 0.82270189839  0.508457735814⎟
⎝0.349877492821 0.508457735814 2.93582296314 ⎠
```
`ans^2`
```⎛6 1 2⎞
⎜1 1 2⎟
⎝2 2 9⎠
```
`SequenceVector(5) @ prime @ sqrt`
`(1.41421356237, 1.73205080757, 2.2360679775, 2.64575131106, 3.31662479036)`