In Tensor and mathematical physics, the Levi-Civita symbol is an entirely antisymmetric tensor that can be used to raise and lower indices of tensors. It is a mathematical tool that is used to define the volume element in n-dimensional space. It is defined as a multi-dimensional array of numbers used to perform operations on other tensors.
In Tensor and Mathematical Physics, the Levi-Civita symbol is used to express the concept of orientation and it’s used to define a cross product, wedge product, and exterior product. It is also used to compute the volume element of an n-dimensional space and to define the Levi-Civita connection (also known as the Christoffel symbols).
We can find the determinant of any matrix by the use of Levi-Civita. Here is how we can find the determinant of the 3 by 3 matrix by using Levi Civita.