| Title: | Working with Matrices over Finite Prime Fields |
|---|---|
| Description: | Provides functions for row-reducing and inverting matrices with entries in many of the finite fields (those with a prime number of elements). With this package, users will be able to find the reduced row echelon form (RREF) of a matrix and calculate the inverse of a (square, invertible) matrix. |
| Authors: | Ryan Higginbottom [aut, cre, cph] |
| Maintainer: | Ryan Higginbottom <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.2.0 |
| Built: | 2024-11-13 06:14:25 UTC |
| Source: | https://github.com/rhigginbottom/matrixmodp |
inv_p() finds the inverse of a square matrix over the field . The function checks for invertibility and then row-reduces the augmented matrix over to find the inverse.
inv_p(A, p)inv_p(A, p)
A |
A square matrix |
p |
A prime integer |
A square matrix of the same size as A
B <- matrix(c(5, 2, 3, 6, 5, 5, 4, 0, 2), 3, 3) inv_p(B, 7) C <- matrix(c(3, 0, 4, 0, 2, 1, 1, 3, 0, 3, 0, 1, 3, 0, 2, 1), 4, 4) inv_p(C, 5)B <- matrix(c(5, 2, 3, 6, 5, 5, 4, 0, 2), 3, 3) inv_p(B, 7) C <- matrix(c(3, 0, 4, 0, 2, 1, 1, 3, 0, 3, 0, 1, 3, 0, 2, 1), 4, 4) inv_p(C, 5)
rref_p() calculates the unique reduced-row echelon form of a matrix with entries in the finite field .
rref_p(A, p)rref_p(A, p)
A |
A matrix |
p |
A prime integer |
A matrix of the same size as A which is the unique reduced-row echelon form of A.
B <- matrix(c(3, 4, 1, 3, 2, 0), 2, 3) rref_p(B, 5) C <- matrix(c(0, 2, 0, 0, 0, 2, 0, 1, 1), 3, 3) rref_p(C, 3)B <- matrix(c(3, 4, 1, 3, 2, 0), 2, 3) rref_p(B, 5) C <- matrix(c(0, 2, 0, 0, 0, 2, 0, 1, 1), 3, 3) rref_p(C, 3)