In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, LHS is informal shorthand for the left-hand side of an
equation
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for ...
. Similarly, RHS is the right-hand side. The two sides have the same value, expressed differently, since
equality
Equality generally refers to the fact of being equal, of having the same value.
In specific contexts, equality may refer to:
Society
* Egalitarianism, a trend of thought that favors equality for all people
** Political egalitarianism, in which ...
is
symmetric
Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...
.
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 either an ''inequality'' (relations "greater than" and "less than", ) or a relation "not equal to" (≠) holds between two values. It is usually written in the form of a pair of expressions den ...
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 equations and integral equation
In mathematical analysis, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,\ldots,x_n ; u(x_1,x_2 ...
s, the terminology ''homogeneous'' is often used for equations with some linear operator
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that pr ...
''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 is the development of mathematics, 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 de ...
, 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
Infix notation is the notation commonly used in arithmetical and logical formulae and statements. It is characterized by the placement of operators between operands—"infixed operators"—such as the plus sign in .
Usage
Binary relations are ...
:''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) or equal sign (American English), also known as the equality sign, is the mathematical symbol , which is used to indicate equality. In an equation it is placed between two expressions that have the same valu ...
References
{{DEFAULTSORT:Sides Of An Equation
Mathematical terminology