Sides of an equation: Difference between revisions
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==Homogeneous and inhomogeneous equations== |
==Homogeneous and inhomogeneous equations== |
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In solving mathematical equations, particularly [[linear simultaneous equations]], [[differential equation]]s and [[integral equation]]s, |
In solving mathematical equations, particularly [[linear simultaneous equations]], [[differential equation]]s and [[integral equation]]s,contrast, an equation with a non-zero RHS is called ''inhomogeneous'' or ''non-homogeneous'', as exemplified by |
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:''Lf'' = ''g'', |
:''Lf'' = ''g'', |
Revision as of 11:30, 1 February 2021
This article needs additional citations for verification. (December 2009) |
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.[1]
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 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 equations,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, 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
References
- ^ Engineering Mathematics, John Bird, p65: definition and example of abbreviation