In
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
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
.
Engineering Mathematics, John Bird, p65
definition and example of abbreviation
More generally, these terms may apply to an inequation or inequality; the right-hand side is everything on the right side of a test operator
In computer science, a relational operator is a programming language construct or operator that tests or defines some kind of relation between two entities. These include numerical equality (''e.g.'', ) and inequalities (''e.g.'', ).
In pro ...
in an expression
Expression may refer to:
Linguistics
* Expression (linguistics), a word, phrase, or sentence
* Fixed expression, a form of words with a specific meaning
* Idiom, a type of fixed expression
* Metaphorical expression, a particular word, phrase, ...
, 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
In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
For example,
:\begin
3x+2y-z=1\\
2x-2y+4z=-2\\
-x+\fracy-z=0
\end
is a system of three equations in t ...
, 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, a ...
s and integral equation
In mathematics, 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,...,x_n ; u(x_1,x_2,x_3,...,x_n ...
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 Map (mathematics), mapping V \to W between two vect ...
''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 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 t ...
, 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
Operator may refer to:
Mathematics
* A symbol indicating a mathematical operation
* Logical operator or logical connective in mathematical logic
* Operator (mathematics), mapping that acts on elements of a space to produce elements of another ...
*. 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 ...
References
{{DEFAULTSORT:Sides Of An Equation
Mathematical terminology