R: n-dimensional Vector Cross Product

CrossN {DescTools} | R Documentation

## n-dimensional Vector Cross Product

### Description

Vector cross product of `n-1` vectors in n-dimensional space

### Usage

    CrossN(A)

### Arguments

`A` | matrix of size `(n-1) x n` where `n >= 2`.

### Details

The rows of the matrix `A` are taken as`(n-1)` vectors in `n`-dimensional space. The cross product generates a vector in this space that is orthogonal to all these rows in `A` and its length is the volume of the geometric hypercube spanned by the vectors.

### Value

a vector of length `n`

### Note

The ‘scalar triple product’ in R^3 can be defined as

`spatproduct <- function(a, b, c) Dot(a, CrossN(b, c))`

It represents the volume of the parallelepiped spanned by the three vectors.

### Author(s)

Hans W. Borchers <hwborchers@googlemail.com>

### See Also

`Cross`, `Dot`

### Examples

    A <- matrix(c(1,0,0, 0,1,0), nrow=2, ncol=3, byrow=TRUE)
    CrossN(A)  #=> 0 0 1

    x <- c(1.0, 0.0, 0.0)
    y <- c(1.0, 0.5, 0.0)
    z <- c(0.0, 0.0, 1.0)
    identical(Dot(x, CrossN(rbind(y, z))), det(rbind(x, y, z)))

[Package DescTools version 0.99.26 Index]