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The null space of spaces of singular matrices. (English) Zbl 0592.15007

Let W be a linear space of \(m\times n\) matrices. The author studies conditions on the dimension of W and the rank of elements in W to the effect that there exists a non-zero vector of length n or m which is annihilated by all the matrices in W or their transposes, respectively. This extends a classical result of J. Dieudonné and solves a problem posed by S. Pierce [ibid. 15, 187-188 (1984)]. An independent solution was also obtained by P. Fillmore, C. Laurie and H. Radjavi [ibid, 18, 255-266 (1985; reviewed below)].
Reviewer: J.Zemánek

MSC:

15A30 Algebraic systems of matrices

Citations:

Zbl 0592.15008
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References:

[1] Lin. and Multilin. Alg. 15 pp 187– (1984)
[2] Dieudonné J., Arch. Math. 1 pp 282– (1948) · Zbl 0032.10601 · doi:10.1007/BF02038756
[3] Flanders H., J. London Math.Soc. 37 pp 10– (1962) · Zbl 0101.25403 · doi:10.1112/jlms/s1-37.1.10
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