p : L 2 ( K ^ ^ ) d → → L 2 ( K ) d , q ^ ^ ↦ ↦ p ( q ^ ^ ) ( x ) := 1 | det ( B ) | ⋅ ⋅ B q ^ ^ ( x ^ ^ ) is called Piola transformation. The usual definition takes the absolute value of the determinant, although some authors make it just the determinant.