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1.5 Binary and Permutation Matrices

Applications of Binary Matrices

Note: if you cannot remember what a binary matrix is, revise notes for 1.1 Matrices: Definition and Unique Cases.

  • Binary matrices are used to represent correlation between datasets. If two categories are correlated, a 1 is placed in the element corresponding to the two, if they are not, a 0 is placed instead.
  • They are also used to represent dominance. If one category is “greater than” another, a 1 is placed in the corresponding element, else a 0 is placed instead.

Note: we will further explore dominance matrices in notes 1.7 Matrix Applications: Dominance Matrices.

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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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