CODEWITHSUNDEEP
rmatrix
Insung Kang
Insung Kang

Reputation: 57

Want to get a matrix inverse without using solve function

I want to find the value of inversed matrix without using a function solve(x).

inversed matrix = 1/det(x)  *  "cofactor"^(transpose)

I know that a determinant of matrix = det(x) and a transpose of matrix = t(x). But I cannot find out how to get cofactor of matrix x and get inversed matrix.

Upvotes: 1

Views: 1811

Answers (2)

Richie Cotton
Richie Cotton

Reputation: 121137

The (i,j)th minor of a matrix is that matrix with the ith row and the jth column removed.

minor <- function(A, i, j)
{
  A[-i, -j]  
}

The (i,j)th cofactor is the (i,j)th minor times -1 to the power i + j.

cofactor <- function(A, i, j)
{
  -1 ^ (i + j) * minor(A, i, j)
}

A word of warning: you shouldn't use this method of calculating inverses of matrices, except for homework purposes, because it is computationally intensive, and (if I recall correctly) not very numerically stable. For real-world purposes use solve or qr.solve or chol2inv. Compare these:

A <- matrix(c(5,1,1,3),2,2)
solve(A)
qr.solve(A)
chol2inv(chol(A))

Upvotes: 4

hd1
hd1

Reputation: 34677

If you have a precomputed cholesky decomposition, chol2inv will sort you.

Upvotes: 1

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