clan A must marry a woman from clan B
clan B must marry a woman from clan C
clan C must marry a woman from clan D
clan D must marry a woman from clan A
Their offspring is born into their fathers clan.
Does the society allow
matrilateral cross cousin marriage?
patrilateral cross cousin marriage?
After how many generations will a man's descendant belong to his clan again?
We can represent possible marriages with the table
| Husband's Clan\Wife's Clan | A | B | C | D |
| A | 0 | 1 | 0 | 0 |
| B | 0 | 0 | 1 | 0 |
| C | 0 | 0 | 0 | 1 |
| D | 1 | 0 | 0 | 0 |
\[M= \left( \begin{array}{cccc} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \end{array} \right)\]
We can represent the tribe taken by children with the matrix
| Husband's Clan\Child's Clan | A | B | C | D |
| A | 1 | 0 | 0 | 0 |
| B | 0 | 1 | 0 | 0 |
| C | 0 | 0 | 1 | 0 |
| D | 0 | 0 | 0 | 1 |
\[C= \left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right)\]
Because
\[C\]
is the identity matrix, it commutes with any other matrix, so \[MC=CM \neq M^TC\]
.If the entry in the ith row and jth column of
\[MC\]
is not 0, then a man of clan i marries a woman of clan k and a man of clan k has children in clan j. Hence \[MC\]
lists the clan of the brother in law's children.If the entry in row i and column j of
\[CM\]
is not 0, is not zero, a man of clan i has children in clan k and a man of clan k marries a woman of clan j. Thus CW list the clan of the son's wife.