TY - JOUR

T1 - Reduction of a pair of skew-symmetric matrices to its canonical form under congruence

AU - Bovdi, Victor A.

AU - Gerasimova, Tatiana G.

AU - Salim, Mohamed A.

AU - Sergeichuk, Vladimir V.

N1 - Funding Information:
The work was supported in part by the UAEU UPAR grants G00001922 and G00002160 .
Funding Information:
The work was supported in part by the UAEU UPAR grants G00001922 and G00002160.
Publisher Copyright:
© 2017 Elsevier Inc.

PY - 2018/4/15

Y1 - 2018/4/15

N2 - Let (A,B) be a pair of skew-symmetric matrices over a field of characteristic not 2. Its regularization decomposition is a direct sum (A__,B__)⊕(A1,B1)⊕…⊕(At,Bt) that is congruent to (A,B), in which (A__,B__) is a pair of nonsingular matrices and (A1,B1),…,(At,Bt) are singular indecomposable canonical pairs of skew-symmetric matrices under congruence. We give an algorithm that constructs a regularization decomposition. We also give a constructive proof of the known canonical form of (A,B) under congruence over an algebraically closed field of characteristic not 2.

AB - Let (A,B) be a pair of skew-symmetric matrices over a field of characteristic not 2. Its regularization decomposition is a direct sum (A__,B__)⊕(A1,B1)⊕…⊕(At,Bt) that is congruent to (A,B), in which (A__,B__) is a pair of nonsingular matrices and (A1,B1),…,(At,Bt) are singular indecomposable canonical pairs of skew-symmetric matrices under congruence. We give an algorithm that constructs a regularization decomposition. We also give a constructive proof of the known canonical form of (A,B) under congruence over an algebraically closed field of characteristic not 2.

KW - Canonical form

KW - Pair of skew-symmetric matrices

KW - Regularization decomposition

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U2 - 10.1016/j.laa.2017.12.013

DO - 10.1016/j.laa.2017.12.013

M3 - Article

AN - SCOPUS:85038825169

SN - 0024-3795

VL - 543

SP - 17

EP - 30

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -