The adjugate of the given polynomial matrix
The adjugate of the given matrix. Also the transpose of the matrix formed from the determinants of submatrices multiplied by the chessboard rule signs.
pMadj(pm)
pm |
a 'polyMatrix' class object |
A polyMatrix class object, the adjugate of the given polynomial matrix.
(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)
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