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

 z Clifford objects

### 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

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