Lie Group
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A Lie group is a differentiable manifold that has the structure of a group and that satisfies the additional condition that the group operations of multiplication and inversion are continuous.
Lie group is a graduate-level concept that would be first encountered in an abstract algebra course.
Prerequisites
| Continuous Function: | A continuous function is function with no jumps, gaps, or undefined points. |
| Group: | A mathematical group is a set of elements and a binary operation that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property. |
| Manifold: | A manifold is a topological space that is locally Euclidean, i.e., around every point, there is a neighborhood that is topologically the same as an open unit ball in some dimension. |
| Matrix: | A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, for every linear transformation, there exists exactly one corresponding matrix, and every matrix corresponds to a unique linear transformation. The matrix is an extremely important concept in linear algebra. |