Max-plus algebra Aλ+
[ap,lam] = maxplusaplus(A)
:is an output matrix of size as the matrix A.
:is an output scalar, this one is an eigenvalue of the matrix A.
The function returns
ap = Aλ⊕ Aλ2 ⊕ Aλ3⊕ ⋯ ⊕ Aλn
where Aλ = -λ ⊗ A , with λ is an an eigenvalue of A, and an error if the matrix A does not has a unique eigenvalue.
If x ∊ GC(A) , where GC(A) is critical path of matrix A, then the column x-th of matrix ap is an eigenvector of A
corresponding to eigenvalue lam.
A=[5 -%inf 5;-%inf 6 3;6 6 3] [ap,lam]=maxplusaplus(A) // We find a critical circuit graph of matrix A // as follows [l,d,x] = maxplusccir(A) // The elemen of x gives information a critical // circuit graph of matrix A. The critical circuit // is: 2 ↔ 2 . So vector v the 2-th column of matrix ap is // an eigenvector of A corresponding to the eigenvalue lam or l. // Indeed this true that A ⊗ v = lam ⊗ v isequal(maxplusotimes(A,ap(:,2)),maxplusotimes(lam,ap(:,2))) | ![]() | ![]() |