Supertropical matrix algebra

Zur Izhakian, Louis Rowen

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


The objective of this paper is to develop a general algebraic theory of supertropical matrix algebra, extending [11]. Our main results are as follows: • The tropical determinant (i. e., permanent) is multiplicative when all the determinants involved are tangible. • There exists an adjoint matrix adj(A) such that the matrix A adj(A) behaves much like the identity matrix (times {divides}A{divides}).• Every matrix A is a supertropical root of its Hamilton-Cayley polynomial fA. If these roots are distinct, then A is conjugate (in a certain supertropical sense) to a diagonal matrix.• The tropical determinant of a matrix A is a ghost iff the rows of A are tropically dependent, iff the columns of A are tropically dependent.• Every root of fA is a "supertropical" eigenvalue of A (appropriately defined), and has a tangible supertropical eigenvector.•

Original languageEnglish
Pages (from-to)383-424
Number of pages42
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Mar 2011
Externally publishedYes


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