classical groups

Classical groups are specific types of mathematical groups that describe symmetries and transformations preserving certain structures in space, such as lengths, angles, or patterns. They include groups like orthogonal groups (preserving distances), unitary groups (preserving complex inner products), and symplectic groups (related to geometry in even-dimensional spaces). These groups are fundamental in areas like geometry, physics, and engineering because they model rotations, reflections, and other symmetry operations, helping us understand how objects behave under different transformations while maintaining specific properties.