In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, LHS is informal shorthand for the left-hand side of an
equation. Similarly, RHS is the right-hand side. The two sides have the same value, expressed differently, since
equality is
symmetric.
Engineering Mathematics, John Bird, p65
definition and example of abbreviation
More generally, these terms may apply to an inequation
In mathematics, an inequation is a statement that an inequality holds between two values. It is usually written in the form of a pair of expressions denoting the values in question, with a relational sign between them indicating the specific in ...
or inequality; the right-hand side is everything on the right side of a test operator in an expression, with LHS defined similarly.
Example
The expression on the right side of the "=" sign is the right side of the equation and the expression on the left of the "=" is the left side of the equation.
For example, in
:
is the left-hand side (LHS) and is the right-hand side (RHS).
Homogeneous and inhomogeneous equations
In solving mathematical equations, particularly linear simultaneous equations, differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
s and integral equations, the terminology ''homogeneous'' is often used for equations with some linear operator ''L'' on the LHS and 0 on the RHS. In contrast, an equation with a non-zero RHS is called ''inhomogeneous'' or ''non-homogeneous'', as exemplified by
:''Lf'' = ''g'',
with ''g'' a fixed function, which equation is to be solved for ''f''. 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
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...
, the homogeneous equation may correspond to a physical theory formulated in empty space, while the inhomogeneous equation asks for more 'realistic' solutions with some matter, or charged particles.
Syntax
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.
See also
* Equals sign
The equals sign (British English, Unicode) or equal sign (American English), also known as the equality sign, is the mathematical symbol , which is used to indicate equality in some well-defined sense. In an equation, it is placed between tw ...
References
{{DEFAULTSORT:Sides Of An Equation
Mathematical terminology