Why is linearity useful

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This article is also available for rental through DeepDyve. View Metrics. Email alerts Article activity alert. Advance article alerts. This is an important measure of sensitivity for mass spectrometers. Factors affecting linearity: Firstly, the ion source behaves linearly only if the ionization efficiency of the analyte is independent of its concentration in the effluent.

As the ionization efficiency of the analyte and its behaviour at different concentrations depends on the used ion source, the linear range s differ between different ion sources. In the ESI source, the linear dependence usually holds at lower concentrations, but at higher concentrations, the excess charge on the surface of the droplets becomes limiting and linearity is lost.

Also the co-eluting compounds can influence the ionization process the so-called matrix effect and lead to the decrease or loss of linearity. Therefore, it is very important to investigate linearity in the presence of matrix compounds. Secondly, during the ion transport from the ion source to the mass analyzer, the number of successfully transported ions must be proportional to the number of ions formed in the source. Collisions or formation of the clusters can also cause losses of ions.

Evaluating linearity near the LOQ combined with repeatability and given specificity can be used to infer trueness. To summarize, linearity is one major aspect in the method validation procedure of assays and quantitative impurity tests.

It provides to assess the range of concentrations for which the method can reliably function. For validation, multi-point calibration techniques are accepted, while single point calibrations are not. In case of a non-linear data set, higher order equations might be transformed or the data must be accepted as they are while demonstrating a clear relation between analyte concentration and response.

Comments powered by CComment. Teilen Sie ihn. Please share. We use cookies on our website. Some of them are essential for the operation of the site, while others help us to improve this site and the user experience tracking cookies. It's a function that is compatible with the two operations. Essentially, such a function is simply taking the field and scaling it, possibly flipping it around as well. In the complex field, the picture is a little more The most intuitive vector spaces - finite dimensional ones over our familiar fields - are basically just multiple copies of the base field, set at "right angles" to each other.

Invertible linear functions now just scale, reflect, rotate and shear this basic picture, but they preserve the algebraic structure of the space. Now, we often work with transformations that do more complicated things that this, but if they are smooth transformations, then they "look like" linear transformations when you "zoom in" at any point.

To analyze something complicated, you have to simplify it in some way, and a good way to simplify working with some weird non-linear transformation is to describe and study the linear transformations that it "looks like" up close. This is why we see linear problems arise so frequently. Some situations are modeled by linear transformations, and that's great.

However, even situations modeled by non-linear transformations are often approximated with appropriate linear maps. The first and roughest way to approximate a function is with a constant, but we don't get a lot of mileage out of that.

The next fancier approach is the approximate with a linear function at each point, and we do get a lot of mileage out of that. If you want to do better, you can use a quadratic approximation.

These are great for describing, for instance, critical points of multi-variable functions. Even the quadratic description, however, uses tools from linear algebra. Edit: I've thought more about this, and I think I can speak further to your question, from comments, "why does the property of linearity make linear functions so "rigid"? You start with evenly spaced points all in straight lines, and after applying a linear map, you still have evenly spaced points, all in straight lines.

Linear maps preserve lattices, in a sense, and that's precisely because they preserve addition and scalar multiplication. Keeping evenly spaced things evenly spaced, and keeping straight lines straight, seems to be a pretty good description of "rigidity". I'll give my two cents, from an applied perspective: what makes linearity so powerful is that linear operations are easily invertible. Maybe this begs the question "well then why can we invert linear functions so easily?

Note that linear algebra is ubiquitous in applications, while module theory is not the only difference is that a module's scalar multiplication is not invertible! The reason is that we frequently need to invert things, and often the only way to go about that is to compute a linear approximation and invert that.

Two examples:. Linear problems are so very useful because they describe well small deviations, displacements, signals, etc. Linear equations have a single solution if one exists. I think this question misses the point slightly.