Name
Abstract | ||
|---|---|---|
We study the generalized eigenproblem A circle times x - lambda circle times B circle times x; where A, B is an element of R-mxn in the max-plus algebra. It is known that if A and B are symmetric, then there is at most one generalized eigenvalue, but no description of this unique candidate is known in general. We prove that if C = A - B is symmetric, then the common value of all saddle points of C (if any) is the unique candidate for lambda. We also explicitly describe the whole spectrum in the case when B is an outer product. It follows that when A is symmetric and B is constant, the smallest column maximum of A is the unique candidate for lambda. Finally, we provide a complete description of the spectrum when n = 2. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/15M1041031 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
matrix,max-plus algebra,generalized eigenproblem,spectrum | Outer product,Combinatorics,Saddle point,Matrix (mathematics),Max-plus algebra,Eigenvalues and eigenvectors,Mathematics,Lambda | Journal |
Volume | Issue | ISSN |
37 | 3 | 0895-4798 |
Citations | PageRank | References |
1 | 0.43 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter Butkovic | 1 | 108 | 25.93 |
| Daniel Jones | 2 | 1 | 0.77 |