({{, (RefLink[ZeroTest, paclet:ref/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.}})

OpenersNotesSection(Spacer1)Details

(RefLink[ZeroTest, paclet:ref/ZeroTest])->(RefLink[Automatic, paclet:ref/Automatic]) effectively tests for zeros using a version of (RefLink[PossibleZeroQ, paclet:ref/PossibleZeroQ]).

OpenersPrimaryExamplesSection(Spacer1)Examples  (1)

OpenersExampleSection0(Spacer1)Basic Examples  (1)

The automatic (RefLink[ZeroTest, paclet:ref/ZeroTest]) used by (RefLink[LinearSolve, paclet:ref/LinearSolve]) does not detect that mat is singular:

szero=Sin[-Sqrt[2-Sqrt[2+Sqrt[2]]]/2]+Sin[Sin[Pi/16]];
mat={{1,0},{1,szero}};
LinearSolve[mat,{1,2}]

szero//FullSimplify

With a stronger zero test, (RefLink[LinearSolve, paclet:ref/LinearSolve]) gives the correct answer:

LinearSolve[mat,{1,2},ZeroTest->(PossibleZeroQ[FullSimplify[#]]&)]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[PossibleZeroQ, paclet:ref/PossibleZeroQ])  ▪  (RefLink[SameTest, paclet:ref/SameTest])  ▪  (RefLink[Eigenvectors, paclet:ref/Eigenvectors])  ▪  (RefLink[Inverse, paclet:ref/Inverse])  ▪  (RefLink[LinearSolve, paclet:ref/LinearSolve])  ▪  (RefLink[MatrixRank, paclet:ref/MatrixRank])  ▪  (RefLink[NullSpace, paclet:ref/NullSpace])  ▪  (RefLink[RowReduce, paclet:ref/RowReduce])}})}})

({{DocumentationFooterIconsRelatedTutorial.png, ({{Tutorials}, {▪(RefLinkPlain[Solving Linear Systems, paclet:tutorial/SolvingLinearSystems])}, {▪(RefLinkPlain[Advanced Matrix Operations, paclet:tutorial/AdvancedMatrixOperations])}})}})