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In the matrix formulation, we are given a nonnegative ''n''×''n'' [[Matrix (mathematics)|matrix]], where the element in the ''i''-th row and ''j''-th column represents the cost of assigning the ''j''-th job to the ''i''-th worker. We have to find an assignment of the jobs to the workers, such that each job is assigned to one worker and each worker is assigned one job, such that the total cost of assignment is minimum.
This can be expressed as permuting the rows and columns of a cost matrix ''C'' to minimize the [[Trace (linear algebra)|trace]] of a matrix:
:<math>
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