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I have a matrix such as this

mat ={{6, 5},{5, 4}}

and I want to find the maximum in every column and minimum in every row. After that I have to get the same number of both. I write this

Max /@ Transpose[mat]

and

Min /@ mat

The results are {6,5} and {5,4}. However I am not sure how I can find that 5 is the same for both. And also it will be good to have all commands to be in one cycle.

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mat = {{6, 5}, {5, 4}};

Those row/column indices i,j for which the minimal row element is the same as the maximal column element is:

Tuples[{Min /@ mat, Max /@ Transpose[mat]}] //
 Position[ArrayReshape[Differences[#, {0, 1}][[All, 1]], Dimensions[mat]], 0] &

{{1, 2}}

| improve this answer | |
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  • $\begingroup$ This code works for row 1 but when I wrote this matt = {{5, 4}, {6, 5}}; the answer is {{1, 4}} but have to be row 2 column 2 . $\endgroup$ – M.Alexis Nov 7 '18 at 18:16
  • $\begingroup$ @M.Alexis I can't reproduce that. Try wrapping With[{mat = matt}, ....] around the code. $\endgroup$ – MeMyselfI Nov 7 '18 at 18:19
  • $\begingroup$ I also tried the solution from @MeMyselfI and it works fine for both matrices, as well as something along the lines of Table[RandomInteger[{0, 10}], {i, 4}, {j, 4}] (it might take a bigger matrix or some repetitions to get something other than a blank table). For a way that is faster than Position see here $\endgroup$ – Titus Nov 8 '18 at 10:53

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