Linearity Definition and 104 Threads

Linearity is the property of a mathematical relationship (function) that can be graphically represented as a straight line. Linearity is closely related to proportionality. Examples in physics include the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships are nonlinear.
Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle.
The word linear comes from Latin linearis, "pertaining to or resembling a line".

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  1. T

    Understanding the Linearity of Determinants: Exploring the Identity Property

    Hi all, I don't understand one thing about linearity of determinants. In the book I have: \det \left( \begin{array}{ccc} . & . & . \\ . & . & . \\ \mbox{[i]} \\ . & . & . \\ . & . & . \\ . & . & . \\ \mbox{[j]} \end{array} \right) = \det \left( \begin{array}{ccc} . & . & . \\ . & . &...
  2. T

    Superposition principle and linearity

    hello folks! this is my first post on the forums and I kick off with an interesting question... I had been coming across the principle of superposition for quite some time and to admit frankly didn't ever understood it. The most abstruse aspect is to comprehend how can to different...
  3. M

    Transforms to acheive linearity

    I was reviewing some statitics and got a little confused with transformations to achieve linearity in bivariate data. The book is really vague and rather than trying to figure it out, I figure someone here will be able to help. I'm not so sure as to what transformations are best applied to which...
  4. Loren Booda

    Math fundamental: can linearity generate reciprocity?

    Does a nontrivial function f(cx) exist such that (d/dx)f(cx)=(1/c)f(cx) and c is constant? "Linearity" here requires that c and x in the function argument preserve their product to the first power.
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