# crossn: n-dimensional Vector Cross Product In pracma: Practical Numerical Math Functions

## Description

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

## Usage

 `1` ```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 â€˜scalar triple productâ€™ 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.

## See Also

`cross`, `dot`

## Examples

 ```1 2 3 4 5 6 7``` ```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))) ```

### Example output

```[1] 0 0 1
[1] TRUE
```

pracma documentation built on Dec. 11, 2021, 9:57 a.m.