ZeroTest
is an option to various linear algebra functions that gives a function to use in testing whether symbolic expressions should be treated as zero.
Examples
Basic Examples (1)
The automatic ZeroTest used by LinearSolve does not detect that mat is non-singular:

With a stronger zero test, LinearSolve gives the correct answer:

Text
Wolfram Research (1988), ZeroTest, Wolfram Language function, https://reference.wolfram.com/language/ref/ZeroTest.html (updated 2007).
CMS
Wolfram Language. 1988. "ZeroTest." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/ZeroTest.html.
APA
Wolfram Language. (1988). ZeroTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ZeroTest.html