[SOLVED] defination of linear element

[maxwell_30]

why is it said that a device having an equation of the form y=mx only for its IV charc is a linear element? why cant it be y=mx+c?

 

[BradtheRad]

In this case the 'mx' equation is a simplified manner of speaking about response of a linear device, when we want to contrast it to exponential (non-linear) response such as x^ .5, or x^2.

There may be circumstances where 'c' enters into the equation. It may be in the form of an unpredictable condition, or an external source, or non-ideal behavior of the component, etc.

However we do not necessarily need a 'c' term for every linear component, or every circumstance. Furthermore non-linear components may need a 'c' term. Then the 'c' term is not specific to linear components, and we can omit 'c'.

 

[c_mitra]

c is a constant term that will force the graph shifted by a simple amount. It will still be a linear form and will be called as such.

Potentials are always relative; you can always add or subtract some constant potential without affecting the broad characteristics. It is the potential difference that matters. Electric field is the gradient of potential - adding a constant term to potential will not affect the electric field. It is the electric field that causes the charges to move from one point to another.

 

[vGoodtimes]

"y = mx + b" is affine, and isn't quite linear. In some contexts, tricks are done to remove the distinction.

In this case, lets take "f(x) = 1*x + 100"

f(2*x) = 2*f(x) for a linear operation
2*x + 100 != 2*(x+100)

f(x+y) = f(x) + f for a linear operation
x + y + 100 != x + 100 + y + 100

 

[c_mitra]

"y = mx + b" is affine, and isn't quite linear.

Affine is mostly used as a transformation: see https://mathworld.wolfram.com/AffineTransformation.html

See the same site about what is linear: https://mathworld.wolfram.com/LinearEquation.html

The above two references are from one of the most respected internet site.

Your definition of a linear operation is not shared by mathematicians: see https://mathworld.wolfram.com/LinearOperator.html

 

[maxwell_30]

okay okay!! So i was mixing up the definitions of a linear equation and a linear operator! Thank u c_mitra & vGoodtimes! that solved my doubt