A monotone matrix is typically defined in the context of certain ordered structures. In matrix theory, a matrix \( A \) is considered monotone if it preserves a certain order under specific conditions.
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A rectangular array whose entries are nondecreasing in each coordinate. Every subarray obtained by restricting to a row interval and a column interval has the same property. Comparing a target with the top-right entry discards a whole row or column, giving staircase matrix search in time linear in the sum of the dimensions.