vector_cross_product {stokes} | R Documentation |
The Vector cross product
Description
The vector cross product \mathbf{u}\times\mathbf{v}
for \mathbf{u},\mathbf{u}\in\mathbb{R}^3
is defined
in elementary school as
\mathbf{u}\times\mathbf{v}=\left(u_2v_3-u_3v_2,u_2v_3-u_3v_2,u_2v_3-u_3v_2\right).
Function vcp3()
is a convenience wrapper for this. However, the
vector cross product may easily be generalized to a product of
n-1
-tuples of vectors in \mathbb{R}^n
, given by
package function vector_cross_product()
.
Vignette vector_cross_product
, supplied with the package, gives
an extensive discussion of vector cross products, including formal
definitions and verification of identities.
Usage
vector_cross_product(M)
vcp3(u,v)
Arguments
M |
Matrix with one more row than column; columns are interpreted as vectors |
u , v |
Vectors of length 3, representing vectors in |
Details
A joint function profile for vector_cross_product()
and
vcp3()
is given with the package at
vignette("vector_cross_product")
.
Value
Returns a vector
Author(s)
Robin K. S. Hankin
See Also
Examples
vector_cross_product(matrix(1:6,3,2))
M <- matrix(rnorm(30),6,5)
LHS <- hodge(as.1form(M[,1])^as.1form(M[,2])^as.1form(M[,3])^as.1form(M[,4])^as.1form(M[,5]))
RHS <- as.1form(vector_cross_product(M))
LHS-RHS # zero to numerical precision
# Alternatively:
hodge(Reduce(`^`,sapply(seq_len(5),function(i){as.1form(M[,i])},simplify=FALSE)))