Changing from one coordinate system to another, more suitable to a particular problem, is a powerful method throughout mathematics. In linear algebra, this might relate to diagonalization or the normal forms of matrices (such as Jordan normal form). In geometry, a change of coordinates might transform a conic’s equation into normal form. In calculus a substitution may simplify an integral. In mechanics, spherical polar coordinates might be better suited for a certain rigid body. In all cases, it is either important that the change of coordinates does not affect a calculation—for example, lengths are invariant under an orthogonal change of variable—or the extent of that change is understood—for example, introducing the Jacobian in multiple integrals.