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1.7 Matrix Applications: Dominance Matrices

Dominance Matrices

  • A dominance matrix is a binary matrix which has individuals listed along the rows and columns. A 1 element indicates the individual corresponding to the row is “dominant to” or “beat” the individual corresponding to the column. A 0 element indicates this is not the case.
  • This type of matrix is useful when modelling systems such as round robin competitions, where multiple people play against each other in rounds, with each round producing a winner.
  • This type of matrix is also known as a one-step dominance matrix.
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1.1 Matrices: Definition and Unique Cases


  • Matrices provide an alternative to ordinary linear algebra which allows us to deal with multi-dimensional data in a more concise way.
  • They are similar in form to a table, with a number of entries arranged into rows and columns.
  • The size of a matrix is expressed in the form rows x columns (i.e. the number of rows followed by the number of columns, with a cross separating them).
  • We can refer to a specific element in a matrix using the name of the matrix, with a subscript listing the row and column corresponding to the element in question e.g. for a matrix; A, the element in the 2nd row and 1st column is denoted by A_{2,1}
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