如何在R编程中手动查找矩阵的次要？

Question

I am supposed to create a function that returns all the minors of a given matrix. I use a for loop to delete the necessary row/column but every time it iterates, it just writes over the previous minor. How can I keep a copy of all the minors? This is what I have so far in the function: (Suppose that b is my given matrix)

minors <- function(b, i, j){
  for(i in 1: nrow(b)){
    for(j in 1: ncol(b)){
      a = b[-i,-j]
    }
  }
  a
}

b = matrix(c(2,3,5,6,7,1,9,4,5), nrow = 3, ncol = 3)
minors(b, i, j)

I'd like to keep the function as simple as possible with just loops. It's also important that I have a way to access the minors individually as I'll be getting each of their cofactors later on.

Any help/tips/advice will be greatly appreciated!!

Answer 1

If you want all the minors, you could use a double for loop as shown below:

minors <- function(b){
  n <- nrow(b)
  a <- matrix(NA, n, n)
  for(i in 1:n)
    for(j in 1:n)
      a[i, j] = det(b[-i, -j])
    a
}
b = matrix(c(2,3,5,6,7,1,9,4,5), nrow = 3, ncol = 3)
minors(b) 
    [,1] [,2] [,3]
[1,]   31   -5  -32
[2,]   21  -35  -28
[3,]  -39  -19   -4

cofactors <- function(b) (-1)^(row(b)+col(b)) *minors(b)
cofactors(b)
     [,1] [,2] [,3]
[1,]   31    5  -32
[2,]  -21  -35   28
[3,]  -39   19   -4