Products of Matrices

  • Thomas J. Laffey
Part of the NATO ASI Series book series (ASIC, volume 333)


We consider the problem of expressing an element A in GL(n, F), where F is a given field, as a product of elements in certain given distinguished subsets of GL(n,F). In particular, we consider the following types of decomposition:
  1. (i)

    A as a multiplicative commutator X -1 Y -1 XY (assuming detA = ±1).

  2. (ii)

    A as a product of involutions (assuming detA = ±1).

  3. (iii)

    A as a product of two involutions (assuming A is similar to A -1).

  4. (iv)

    A as a product of a symmetric matrix by an involution.

  5. (v)

    A as a product of skew-symmetric matrices.


While most of the discussion concerns matrices over a field, we refer briefly to the case where the matrices in question have integer entries.


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Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Thomas J. Laffey
    • 1
  1. 1.Department of MathematicsUniversity College DublinBelfieldIreland

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