Fedeew-Leverrier

Adjoint matrix and Characteristic Polynomial

adjoint(A)

charpoly(A)

Arguments

A	a square matrix

Value

adjoint returns the adjoint matrix of A charpoly returns the coefficients of the characteristic polynomial of A as a vector.

Details

These functions compute the adjoint matrix and characteristic polynomial of A by the Fedeew-Leverrier algorithm.

If A has integer elements and the computations are performed with integer arithmetic the result is exact.

Examples

edges <- parse.digraph(c(
  "E *-> D",
  "D *-> C",
  "C -> E",
  "E *-> B",
  "B *-> A",
  "A -> E",
  "D -> B"))
edges <- enforce.limitation(edges)
A <- adjacency.matrix(edges,labels=TRUE)
adjoint(A)
#>   [,1] [,2] [,3] [,4] [,5]
#> A    5    2    2    1    3
#> B    1    2    2    1    3
#> C    2    0    4    2    2
#> D    2    0    0    2    2
#> E    4    0    4    0    4