Reexpress

Reexpress is the act of expressing something in a different form or representation. It involves rewriting a given object—such as a function, equation, or dataset—using an alternative set of variables, basis, or encoding while preserving its meaning or value. The goal is often to reveal useful structure, simplify calculations, or improve interpretability.

In mathematics, reexpression refers to rewriting a mathematical object in a new form. This can include changing variables, adopting a different basis in linear algebra, or presenting a function in a canonical or simplified form. For example, a vector can be reexpressed in a different coordinate system, or a polynomial can be reexpressed through a substitution to make properties like symmetry or roots more apparent. Substitution and change of variables are common techniques that reexpress expressions to facilitate integration, differentiation, or solving equations.

In analysis and geometry, reexpression can help transform problems to more tractable coordinates or to align with constraints such as boundary conditions. In linear algebra, reexpressing a matrix in a new basis (for instance, through diagonalization) can illuminate eigenvalues and dynamic behavior. In statistics and machine learning, reparameterization or reexpressing a model can improve numerical stability, convergence of algorithms, or interpretability.

Limitations include potential increases in algebraic or computational complexity, and not all reformulations yield simplifications. Reexpress is closely related to concepts such as change of basis, reparameterization, and symbolic computation. It is a general, non-technical term used across disciplines to describe the process of presenting the same content in an alternative, often more advantageous, form.