Beasley, LeRoy B. The null space of spaces of singular matrices. (English) Zbl 0592.15007 Linear Multilinear Algebra 18, 249-254 (1985). 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 Cited in 1 ReviewCited in 3 Documents MSC: 15A30 Algebraic systems of matrices Keywords:null space; singular matrices; common eigenvectors; of a subspace of matrices; linear space of matrices; rank Citations:Zbl 0592.15008 PDFBibTeX XMLCite \textit{L. B. Beasley}, Linear Multilinear Algebra 18, 249--254 (1985; Zbl 0592.15007) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.