Please note: This PhD seminar will be given online.
Stavros
Birmpilis,PhD
candidate
David
R.
Cheriton
School
of
Computer
Science
Supervisors: Professors George Labahn, Arne Storjohann
Given a nonsingular integer matrixA ∈ Z×with Smith normal formS= diag(s1, . . . ,sn), we define a matrixM ∈ Z×to be a Smith massager forA. We use the notationcǻSto show that an equivalence is taken column modulo the diagonal entries inS. MatrixMsatisfies (i) thatAM≡ 0cǻS, namely, the matrix AMS−1is integral, and (ii) that there exists a matrixW∈ Z×such thatWM ≡ IncǻS, namely, the Smith massager is “unimodular” up to equivalence column moduloS. We obtain the Smith massager from an algorithm that computes the Smith form ofA. We show thatMserves as a useful object for tackling other problems in integer linear algebra like computing the Smith multiplier matrices forAor representing the fractional part of the adjoint ofA.
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