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The element in the diagonal of a matrix by which other elements are divided in an algorithm such as Gauss-Jordan Elimination is called the pivot element. Partial pivoting is the interchanging of rows and full pivoting is the interchanging of both rows and columns in order to place a particularly ``good'' element in the diagonal position prior to a particular operation.
See also Gauss-Jordan Elimination
References
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England:
Cambridge University Press, pp. 29-30, 1992.