RConics (version 1.0)

(i,j)-cofactor and (i,j)-minor: \((i,j)\)-cofactor and \((i,j)\)-minor of a matrix

Description

Compute the \((i,j)\)-cofactor, respectively the \((i,j)\)-minor of the matrix \(A\). The \((i,j)\)-cofactor is obtained by multiplying the \((i,j)\)-minor by \((-1)^{i+j}\). The \((i,j)\)-minor of \(A\), is the determinant of the \((n - 1) \times (n - 1)\) matrix that results by deleting the \(i\)-th row and the \(j\)-th column of \(A\).

Usage

cofactor(A, i, j)
minor(A, i, j)

Arguments

A

a square matrix.

i

the \(i\)-th row.

j

the \(j\)-th column.

Value

The \((i,j)\)-minor/cofactor of the matrix \(A\) (single value).

See Also

adjoint

Examples

# NOT RUN {
  A <- matrix(c(1,4,5,3,7,2,2,8,3),nrow=3,ncol=3)
  A
  minor(A,2,3)
  cofactor(A,2,3)

# }