magnitude {clifford} | R Documentation |

## Magnitude of a clifford object

### Description

Following Perwass, the magnitude of a multivector is defined as

\[\left|\left|A\right|\right| = \sqrt{A\ast A}\]

Where \(A\ast A\) denotes the Euclidean scalar product
`eucprod()`

. Recall that the Euclidean scalar product is never
negative (the function body is `sqrt(abs(eucprod(z)))`

; the
`abs()`

is needed to avoid numerical roundoff errors in
`eucprod()`

giving a negative value).

### Usage

```
## S3 method for class 'clifford'
Mod(z)
```

### Arguments

### Note

If you want the square,
\(\left|\left|A\right|\right|^2\) and not
\(\left|\left|A\right|\right|\), it is faster and more accurate
to use `eucprod(A)`

, because this avoids a needless square root.

There is a nice example of scalar product at `rcliff.Rd`

.

### Author(s)

Robin K. S. Hankin

### See Also

`Ops.clifford`

,
`Conj`

,
`rcliff`

### Examples

```
Mod(rcliff())
# Perwass, p68, asserts that if A is a k-blade, then (in his notation)
# AA == A*A.
# In package idiom, A*A == A %star% A:
A <- rcliff()
Mod(A*A - A %star% A) # meh
A <- rblade()
Mod(A*A - A %star% A) # should be small
```

[Package

*clifford* version 1.0-8

Index]