Feng, Xinlong; Zhang, Zhinan The rank of a random matrix. (English) Zbl 1162.15015 Appl. Math. Comput. 185, No. 1, 689-694 (2007). Summary: This work is concerned with the numerical rank of a matrix in matrix computations. We conclude that a real random matrix has full rank with probability 1 and a rational random matrix has full rank with probability 1, too. Finally, the applications of the numerical matrix are given. Cited in 10 Documents MSC: 15B52 Random matrices (algebraic aspects) 15A03 Vector spaces, linear dependence, rank, lineability 15A12 Conditioning of matrices Keywords:random matrix; defective rank; numerical rank; condition number PDF BibTeX XML Cite \textit{X. Feng} and \textit{Z. Zhang}, Appl. Math. Comput. 185, No. 1, 689--694 (2007; Zbl 1162.15015) Full Text: DOI References: [1] Golub, G.H.; Vanloan, C.F., Matrix computations, (1996), Hopkins press [2] Golub, G.H.; Wilkinson, J.H., Ill-conditioned eigensystem and the computation of the Jordan canonical form, SIAM rev., 18, October, 578-619, (1976) · Zbl 0341.65027 [3] Kaltonfen, E.; Krishnamoothy, M.F.; Saunders, B.C., Parallel algorithms for matrix normal forms, Linear algebra appl., 136, (1990) [4] Li, T.Y.; Zhang, Zhinan; Wang, Tianjun, Determining the structure of the Jordan normal form of a matrix by symbolic computation, Linear algebra appl., 252, 221-257, (1997) · Zbl 0870.65030 [5] Zhang, Zhinan, The Jordan form of a real random matrix, numerical mathematics, J. chin. univ., 23, 4, 363-367, (2001) · Zbl 0992.15008 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.