极坐标线性代数基础

This research introduces a structured framework called Polar Linear Algebra, based on polar geometry, which combines a linear radial component with a periodic angular component to revisit operator learning from a spectral perspective. The associated operators are defined, and their spectral properties are analyzed. To demonstrate feasibility, the framework is evaluated on a canonical benchmark dataset (MNIST). Despite the simplicity of the task, results indicate that polar and fully spectral operators can be trained reliably, and imposing self-adjoint-inspired spectral constraints enhances stability and convergence. Beyond accuracy, the proposed formulation leads to a reduction in parameter count and computational complexity.