Difference between revisions of "Linear"

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A function <math>f</math> is linear iff <math>f(x) - f(y)</math> depends only on <math>x - y</math>. The notion of linearity, although normally defined in spaces like <math>\mathbf{R}</math>, can be extended to arbitrary [[vector space|vector spaces]].
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A function <math>f</math> is linear if <math>f(x) - f(y)</math> depends only on <math>x - y</math>. The notion of linearity, although normally defined in spaces like <math>\mathbf{R}</math>, can be extended to arbitrary [[vector space|vector spaces]].
  
 
== Examples of linear functions ==
 
== Examples of linear functions ==

Latest revision as of 00:11, 23 April 2024

A function $f$ is linear if $f(x) - f(y)$ depends only on $x - y$. The notion of linearity, although normally defined in spaces like $\mathbf{R}$, can be extended to arbitrary vector spaces.

Examples of linear functions

  • $f(x, y) := 2 + 55x + 592y$
  • $g(x) := 1 + 2x$

See also

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