I'm confused about the concept of pivoting a Matrix element. This operation seems to be a fundamental operation which is used as part of more complex operations such as inverting a matrix.
However, the definition of pivoting, and what it entails, seems to vary depending on the context.
In the context of inverting a matrix, for example, pivoting entails changing the pivot element to
1, and then all other elements in the same column to
0 (and appropriately adjusting the other elements in the same row/column.) However, other times the definition of pivoting only involves changing other elements in the same column to
0, while leaving the pivot element as it is.
Is there a universal definition of pivoting, or is it simply a casual term which changes depending on context? Or, to put it another way: must the pivot element always be a