R - 计算向量的叉积(物理)

Question

我究竟做错了什么？

> crossprod(1:3,4:6)
     [,1]
[1,]   32

根据本网站: http://onlinemschool.com/math/assistance/vector/multiply1/

它应该给出:

{-3; 6; -3}

另见 What is R's crossproduct function?

Answer 1

这是一个广义的交叉产品:

xprod <- function(...) {
  args <- list(...)

  # Check for valid arguments

  if (length(args) == 0) {
    stop("No data supplied")
  }
  len <- unique(sapply(args, FUN=length))
  if (length(len) > 1) {
    stop("All vectors must be the same length")
  }
  if (len != length(args) + 1) {
    stop("Must supply N-1 vectors of length N")
  }

  # Compute generalized cross product by taking the determinant of sub-matricies

  m <- do.call(rbind, args)
  sapply(seq(len),
         FUN=function(i) {
           det(m[,-i,drop=FALSE]) * (-1)^(i+1)
         })
}

对于您的示例:

> xprod(1:3, 4:6)
[1] -3  6 -3

这适用于任何维度:

> xprod(c(0,1)) # 2d
[1] 1 0
> xprod(c(1,0,0), c(0,1,0)) # 3d
[1] 0 0 1
> xprod(c(1,0,0,0), c(0,1,0,0), c(0,0,1,0)) # 4d
[1]  0  0  0 -1

见 https://en.wikipedia.org/wiki/Cross_product