Congruence of symmetric matrices over local rings |
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| Authors: | Yonglin Cao Fernando Szechtman |
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| Institution: | aInstitute of Applied Mathematics, School of Sciences, Shandong University of Technology, Zibo, Shandong 255091, PR China;bDepartment of Mathematics and Statistics, University of Regina, Saskatchewan, Canada |
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| Abstract: | Let R be a commutative, local, and principal ideal ring with maximal ideal  and residue class field F. Suppose that every element of  is square. Then the problem of classifying arbitrary symmetric matrices over R by congruence naturally reduces, and is actually equivalent to, the problem of classifying invertible symmetric matrices over F by congruence. |
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| Keywords: | Matrix congruence Bilinear form Local ring Principal ideal ring |
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