polyMatrix (version 0.2.5)

pMadj: The adjugate of the given polynomial matrix

Description

The adjugate of the given matrix. Also the transpose of the matrix formed from the determinants of submatrices multiplied by the chessboard rule signs.

Usage

pMadj(pm)

Arguments

pm

a 'polyMatrix' class object

Value

A polyMatrix class object, the adjugate of the given polynomial matrix.

See Also

pMdet, pMsub

Examples

# NOT RUN {
(A<-polyMgen.a(2,2))
# 1 + 2*x + 3*x^2           7 + 8*x + 9*x^2 + 10*x^3
# 4 + 5*x + 6*x^2           11 + 12*x
pMdet(A)
# -17 - 33*x - 61*x^2 - 97*x^3 - 104*x^4 - 60*x^5
pMsub(A,1,1)*pMsub(A,2,2)-pMsub(A,1,2)*pMsub(A,2,1)
# -17 - 33*x - 61*x^2 - 97*x^3 - 104*x^4 - 60*x^5
(B<-pMadj(A))
# 11 + 12*x                  -7 - 8*x - 9*x^2 - 10*x^3
#  -4 - 5*x - 6*x^2           1 + 2*x + 3*x^2
A*B         # diagonal
pMdet(A)

B*A
pMdet(A)

# real matrices

X<-matrix(c(3,0:7), ncol = 3)
X
#   3    2    5
#   0    3    6
#   1    4    7

det(X) # -12
solve(X)*det(X)
#  -3    6   -3
#   6   16  -18
#  -3  -10    9
pMadj(M2pM(X)) # the same

# clean up
# rm(A, B, X)

# }