pivot position_矩阵里的pivot是什么？请解释详细

elliot

回答于：2017-11-26

一般翻译为“主元”，在对矩阵做某种算法时，首先进行的部分元素。在线性规划的单纯形法中常见。

wiki的解释如下：

Pivot element

(the first element distinct from zero in a matrix in echelon form)

The pivot or pivot element is the element of a matrix, which is selected first by an algorithm (e.g. Gaussian elimination, Quicksort, Simplex algorithm), to do certain calculations with the matrix.

The above mentioned matrix algorithms require an entry distinct from zero in pivot position to work properly or at all respectively. Depending on the algorithm either one (random) element distinct from zero or the element with the greatest absolute value in a row or column is chosen. This is called pivotization. The row containing the pivot element is called pivot row, the pivot element’s column is called pivot column.

Pivot element in Quicksort means the element that is selected as boundary for partitioning. Quicksort sorts all elements „left“ and „right“ of the pivot element recursively.