Lsym
Lsym is a shorthand used in some mathematical literatures to denote symmetry-related structures associated with linear or Lie symmetries of a system. It is not a universally fixed term, but in common usage it refers to symmetry entities that can be exploited to simplify or solve problems.
In differential equations and mathematical physics, Lsym most often denotes the Lie symmetry algebra of a differential
In linear algebra contexts, Lsym can denote a linear symmetric operator or a symmetric matrix, i.e., a
Computation typically involves solving determining equations for point or contact symmetries, or verifying symmetry of a
Applications include reduction of differential equations, construction of invariant solutions, and, where appropriate, spectral decompositions in
See also Lie group, Lie algebra, symmetry, Noether's theorem, differential equation, invariant.