A relation among a group of people is called a dominance relation
if the associated incidence matrix A has the property that for all distinct
pairs i and j, Aij = 1 if and only if Aji = 0, that is,
given any two people, exactly one of them dominates (or, using the terminology of
our first example, can send a message to) the other. Since A is an incidence
matrix, Aii = 0 for all i.
For such a relation, it can be shown (see Exercise 21)
that the matrix A + A2 has a row [column] in which each entry is positive
except for the diagonal entry.
Prove that the matrix A + A2 has a row [column] in which each
entry is positive except for the diagonal entry:
網路解答:
https://imgur.com/WSTiYfw
我重寫:
https://imgur.com/dkYe2Wh
對網路解答做了重寫，解答某些部分寫得有點模糊+typo
所以不確定修改後是否是解答的原意，是否正確? 尤其是4.
謝謝
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