(n.) A particular element of a matrix during some algorithm. Many matrix algorithms need carefully chosen pivots to improve their numerical accuracy and stability. Pivoting involves arranging that the pivotal element has an appropriate numerical value by reordering and/or swapping rows and columns in the matrix.
Pivot has two meanings: A pivot of a matrix which has been reduced to echelon form is the leading non-zero element in each row. (We also refer to the pivots of a matrix which has not been reduced, referring implicitly to its echelon form.) When performing Gaussian Reduction on a matrix, reducing it to echelon form or reduced echelon form, the act of pivoting is to perform a row swap (partial pivoting) or both a row and a column swap (total pivoting), in order to bring as large an element as possible into the pivot position. This can reduce accumulated error when performing numerical operations on large matrices. Synonyms: Related
Also Rotate. An OLAP function. It is an operation whereby the the dimensional orientation of a report or page display is changed. For example, pivoting may consist of swapping the rows and columns, or moving one of the row dimensions into the column dimension, or swapping an off-spreadsheet dimension with one of the dimensions in the page display (either to become one of the new rows or columns), etc. A specific example of the first case would be taking a report that has Time across (the columns) and Products down (the rows) and rotating it into a report that has Product across and Time down. An example of the second case would be to change a report which has Measures and Products down and Time across into a report with Measures down and Time over Products across. An example of the third case would be taking a report that has Time across and Product down and changing it into a report that has Time across and Geography down.