Linear Function (original) (raw)

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• Algebra
• Linear Algebra
• General Linear Algebra
• Calculus and Analysis
• Functions

In calculus, geometry, and plotting contexts, the term "linear function" means a function whose graph is a straight line, i.e., a polynomial function of degree 0 or 1. A linear function in one variable therefore has the form

	(1)

while a linear function in variables has the form

	(2)

In linear algebra and functional analysis, a linear function is a function which satisfies the linearity conditions

	(3)

and

	(4)

for all and in the domain and all scalars .

See also

Bilinear Function, Function, Line, Linear Functional,Piecewise Linear Function, Polynomial Function, Vector Space Explore this topic in the MathWorld classroom

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Cite this as:

Weisstein, Eric W. "Linear Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LinearFunction.html

Subject classifications

• Algebra
• Linear Algebra
• General Linear Algebra
• Calculus and Analysis
• Functions