- Sides of an equation
In
mathematics , LHS is informal shorthand for the left-hand side of anequation . Similarly, RHS is the right-hand side. Each is solely a name for a term as part of an expression; and they are in practice interchangeable, since equality is symmetric. This abbreviation is seldom if ever used in print; it is very informal.More generally, these terms may apply to an
inequation orinequality . In the "inequality case", there is no symmetry. The right-hand side is everything on the right side of atest operator in an expression. Conversely, the left-hand side is everything on the left side.ome examples
In
:2"a" + 5 = "a"/3,
the term
:"a"/3
is the RHS.
In
:"x" ≤ 10,
just
:10
is the RHS.
Homogeneous and inhomogeneous equations
In solving mathematical equations, particularly
linear simultaneous equations ,differential equation s andintegral equation s, the terminology "homogeneous" is often used for equations with the RHS set equal to zero. The corresponding "inhomogeneous" or "nonhomogeneous" equation then has the RHS with some given data, but of a general character.The typical case is of some
operator "L", with the difference being that between the equation:"Lf" = 0,
to be solved for a function "f", and the equation
:"Lf" = "g",
with "g" a fixed function, to solve again for "f". The point of the terminology appears for "L" a
linear operator . Then any solution of the inhomogeneous equation may have a solution of the homogeneous equation added to it, and still remain a solution.For example in
mathematical physics , the homogeneous equation may correspond to a physical theory formulated inempty space , while the inhomogeneous equation asks for more 'realistic' solutions with some matter, or charged particles.yntax
More abstractly, when using
infix notation :"T"*"U"
the term "T" stands as the left-hand side and "U" as the right-hand side of the
operator *. This usage is less common, though.ee also
*
equal sign
Wikimedia Foundation. 2010.