Exact matrix algebra for matrices with rational entries.
# a rational matrix
M
## [,1] [,2] [,3] [,4]
## [1,] "7" "4/7" "1/4" "2/3"
## [2,] "3/5" "2" "3/2" "3/4"
## [3,] "10/3" "10" "7" "1"
## [4,] "1" "5/2" "1/3" "7/2"
# determinant
Qdet(M)
## [1] "-227405/3024"
# inverse
Qinverse(M)
## [,1] [,2] [,3] [,4]
## [1,] "6678/45481" "-2274/45481" "2901/454810" "-4338/227405"
## [2,] "-17892/227405" "-491624/227405" "510993/1137025" "397782/1137025"
## [3,] "9324/227405" "666168/227405" "-525726/1137025" "-572424/1137025"
## [4,] "2352/227405" "290964/227405" "-316998/1137025" "101448/1137025"
# check
library(gmp)
as.bigq(M) %*% as.bigq(Qinverse(M))
## Big Rational ('bigq') 4 x 4 matrix:
## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 0
## [2,] 0 1 0 0
## [3,] 0 0 1 0
## [4,] 0 0 0 1
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