The Levi-Civita symbol

The Levi-Civita symbol is a mathematical tool used to describe the orientation of coordinate systems, especially in three dimensions. It assigns a value of +1 or -1 depending on the order of three indices (like x, y, z), reflecting whether they follow a right-handed or left-handed system, or is zero if any two indices are the same. In essence, it helps identify how components are arranged relative to each other, crucial in vector calculus, physics, and engineering for operations like cross products and rotation descriptions.