Right-hand side
   HOME

TheInfoList



OR:

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 Equality may refer to: Society * Political equality, in which all members of a society are of equal standing ** Consociationalism, in which an ethnically, religiously, or linguistically divided state functions by cooperation of each group's elit ...
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 definiti ...
.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 Inequality may refer to: Economics * Attention inequality, unequal distribution of attention across users, groups of people, issues in etc. in attention economy * Economic inequality, difference in economic well-being between population groups * ...
; the right-hand side is everything on the right side of a test operator 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, o ...
, 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 : x + 5 = y + 8 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, an ...
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 ''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 developme ...
, 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