主元（英语：pivot或pivot element）是矩阵、数组或是其他有限集合的一个演算元素，算法（如高斯消去法, 快速排序, 单纯形法等等）首先选出主元，用于特定计算。

在矩阵算法中，主元必须是非零元素，甚至是距零最远的元素（绝对值最大）。寻找主元的过程被称为pivoting。随后把主元所在的行（或列）交换到固定位置，用于随后的计算。主元所在的列组成列空间的一个基。但实际的算法很少移动矩阵的行，因为这对于大矩阵（含有几千到几百万的行与列）将招致极大的时间花费；替代的办法是仅仅记录矩阵的行的交换信息。

The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm, etc.), to do certain calculations. In the case of matrix algorithms, a pivot entry is usually required to be at least distinct from zero, and often distant from it; in this case finding this element is called pivoting. Pivoting may be followed by an interchange of rows or columns to bring the pivot to a fixed position and allow the algorithm to proceed successfully, and possibly to reduce round-off error. It is often used for verifying row echelon form.