A **max-plus algebra** is a semiring over the union of real numbers and

## Contents

## Scalar operations

Let *a* and *b* be real scalars or ε. Then the operations maximum (implied by the **max** operator
**plus** operator

**Watch**: Max-operator

## Matrix operations

Max-plus algebra can be used for matrix operands **A**, **B** likewise, where the size of both matrices is the same. To perform the **A**
**B** - operation, the elements of the resulting matrix at (row i, column j) have to be set up by the maximum operation of both corresponding elements of the matrices **A** and **B**:

The
**A**
**B** - operation, where **A** is a *m*×*p* matrix and **B** is a *p*×*n* matrix, the elements of the resulting matrix at (row i, column j) are determined by matrices **A** (row i) and **B** (column j):

## Useful enhancement elements

In order to handle marking times like

To point the zero number out, the element *e* was defined by

Obviously, ε is the neutral element for the
*e* is for the

## Algebra properties

## Additional reading

*Max-linear Systems: Theory and Algorithms*, Springer Monographs in Mathematics, Springer-Verlag, doi:10.1007/978-1-84996-299-5