Matrix Lie Group

Matrix Lie groups, mathematical structures representing continuous symmetries, are central to modeling systems with rotational or other geometric transformations, such as robotic systems and image processing. Current research focuses on developing efficient algorithms for tasks like Kalman filtering, smoothing, and trajectory optimization within these group frameworks, often leveraging invariant representations to improve accuracy and consistency. This work is significant because it enables more robust and accurate estimation and control in applications where traditional methods struggle with nonlinearity and uncertainty, impacting fields ranging from robotics and computer vision to quantum computing.