Index Matrices: Definitions, Operations, Relations - Index Matrices: Towards an Augmented Matrix Calculus - page 24

de
a 10
b 10
d 01

E ⊗ max F = ,

with sub-operation “min” is

de
a 00
b 10
d 01

E ⊗ min F =

and it has, respectively, the graph-forms

( , )

In addition, we mention that the graph-representation of the 0 1 -IM

cde f gi
a 000000
b 010000
c 000000
d 001000
e 000000
f 000000
h 000000

E ⊕ min F =

and in the reduced form

de
b 10
d 01

E min F =

i.e., the graph form is

If we like to omit some vertex of a graph, we can do this, using operation “reduc-
tion”. For example,