The geometric Laplace transform: Definition, existence and properties of the Geometric Algebra Laplace transform
Extending a classic math tool to work with geometric algebra
Researchers have defined the Laplace transform—a fundamental mathematical tool for solving differential equations—to work within geometric algebra, a system that handles multidimensional spaces and rotations. This extension applies to geometric algebras with signature 5 or lower, filling a gap needed for modeling and controlling real-world systems like electrical circuits.
Engineers designing electrical circuits and other dynamical systems increasingly want to use geometric algebra because it naturally represents rotations and multidimensional transformations. Without a properly defined Laplace transform in this framework, they have to convert between different mathematical systems, losing efficiency and clarity. This work removes that barrier, letting engineers stay within geometric algebra from problem setup through solution.