magnitude: Magnitude of a clifford object

In clifford: Arbitrary Dimensional Clifford Algebras

Magnitude of a clifford object

Description

\loadmathjax

Following Perwass, the magnitude of a multivector is defined as

\mjdeqn\left

|\left|A\right|\right| = \sqrtA\ast Aomitted; see PDF

Where \mjeqnA\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, \mjeqn\left|\left|A\right|\right|^2||A||^2 and not \mjeqn\left|\left|A\right|\right|||A||, 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

clifford documentation built on Aug. 14, 2022, 1:05 a.m.