I want to implement LARGE() function without changing the matrix while assigning zero to diagonal elements which can be achieved through =IF(ROW()=COLUMN(),0,"") if the change of base matrix is allowed.
Assign zero to diagonal cells without changing the matrix in Excel
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Use the MAP function to create a new array from your array. Use your IF logic in the LAMBDA formula. This creates an array where all the diagonals are zeros:
Put that inside your LARGE formula, so this would take the 10th largest value from the new array: