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The phrase "a linear dependence of" is correct and usable in written English.
It is typically used in mathematical or scientific contexts to describe a relationship where one vector can be expressed as a linear combination of others.
Example: "In linear algebra, we often analyze a linear dependence of vectors to determine if they span a certain space."
Alternatives: "a linear relationship among" or "a linear correlation of".
Exact(60)
A linear dependence of the limit of linearity on S/ V of the microfluidic detection cell was found.
A linear dependence of photocurrent on cation radius was revealed.
A linear dependence of rate on pressure was found.
The results show a linear dependence of friction on load confirming the Coulomb law.
Once again, a linear dependence of reaction time upon angle was found, suggesting smooth, regular rotation of an image.
Simulation results show a linear dependence of the fiber birefringence with temperature.
Pawlowski and Ridley (2011) reported a linear dependence of neutral density response on the total integrated energy.
f A linear dependence of the discharge current density on the scan rate up to 5000 mV s−1.
The regression plots showed a linear dependence of RSFI values on drug concentration over the range cited in Table 1.
A linear dependence of I L on Pexc demonstrates the absence of temperature-activated non-radiative decay in the material.
A linear dependence of σDC(P) on V−1h(P) was also found.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com