= Erwin H. Bareiss
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<Erwin H. Bareiss> developed integer-preserving methods for <Gaussian elimination>. The <Bareiss algorithm> uses determinant identities to arrange divisions that are exact, reducing the growth of intermediate rational expressions.<Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination by Erwin H. Bareiss>[Original byline, section I, equations 3, 6 and 8]{ref}
An update combines two products and divides by a previous pivot. The reason this stays in the integers is structural: the quantities represent related minors satisfying <Sylvester identity for bordered minors>. This makes exact <linear algebra> practical without replacing the calculation by floating-point approximation.<Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination by Erwin H. Bareiss>[Pages 565–567]{ref}
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