Greenwood press

62
MATRICES

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Linear programming uses algorithms such as the simplex method to compute
the most profitable solution from matrices of production. Matrices also structure
inquiry into situations that have competing players with multiple choices of
action. The outcomes can be organized into matrices that use players for rows
and options for columns. Game theorists have developed mathematical strategies
for transforming the matrices in a way that gives each player the best outcome,
or in a way that avoids worst outcomes. Game strategies have been used to ana-
lyze competition for food, to determine which students get the last seats in col-
lege courses, to resolve conflicts in classrooms, and to select the best choices for
potentially warring nations. The importance of game theory for the study of eco-
nomic behavior is recognized by the awarding of the Nobel prize. The 1994
award in economics went to John Nash, John C. Harsanyi, and Reihard Selten for
their contributions to game theory. Other Nobel awards related to game theory
have been those in 1996 to William Vickrey and James Mirrlees, and to Herbert
Simon in 1979. However, these were not the first Nobel prizes to recognize work
with matrices. In 1973, Wassily Leontief won the prize for his prediction of best
economic strategies from large input–output matrices. Leontief’s theories were
the basis for U.S. government policies that resulted in effective industrial pro-
duction during World War II.
online sources for further exploration
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David Levine’s Zero Sum Game Solver

Cryptology and coding


Electronics

Image rotation

Logging

Markov chains

Matrices in chemistry

Matrix model activities

Stability of structures