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Matrix-Set

By Kardi Teknomo, PhD.

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Matrix-Set

To derive the formulation in the paper, we use a combination of both matrix and set operations. In contrast to ordinary matrices in linear algebra whose elements are numbers or scalar values (which we call matrix-count), it is necessary to create our own mathematical concept of a matrix-set which is a matrix whose elements are sets. We use tilde on the top of a matrix to indicate matrix-set, such as Flow-set matrix and OD-set matrix. Operations on matrix-set are similar to both operations in matrix and set theory where the members in each matrix element must be unique and the order of the elements in a set is not important. We also extend the Hadamard multiplication to involve a matrix-set and a binary matrix. The Hadamard product between a matrix set and a binary matrix is computed by multiplication of corresponding elements, resulting either in the original element of the matrix set (if multiplied with 1) or an empty set (if multiplied by 0).  We have developed special numerical library of matrix-set to serve the purpose of this research.

Preferable reference for this tutorial is

Teknomo, Kardi. (2013) Relationship between Generalized Origin Destination and Flow Matrix – A Tutorial
http://people.revoledu.com/kardi/research/trajectory/od/