On the nonsingularity of complex matrices
نویسندگان
چکیده
منابع مشابه
Checking nonsingularity of tridiagonal matrices
I. Bar-On, B. Codenotti, and M. Leoncini presented a linear time algorithm for checking the nonsingularity of general tridiagonal matrices [BIT, 36:206, 1996]. A detailed implementation of their algorithm, with some extensions to possibly reducible matrices, is further described in the present paper.
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We derive necessary and sufficient conditions for guaranteeing the nonsingularity of a block two-by-two matrix by making use of the singular value decompositions and the Moore-Penrose pseudoinverses of the matrix blocks. These conditions are complete, and much weaker and simpler than those given by Decker and Keller (J. Math. Anal. Appl. 75(1980)417-430), and may be more easily examined than th...
متن کاملOn Nonsingularity of Linear Combinations of Tripotent Matrices
Let T1 and T2 be two commuting n × n tripotent matrices and c1, c2 two nonzero complex numbers. The problem of when a linear combination of the form T = c1T1 + c2T2 is nonsingular is considered. Some other nonsingularitytype relationships for tripotent matrices are also established. Moreover, a statistical interpretation of the results is pointed out.
متن کاملEla Checking Nonsingularity of Tridiagonal Matrices Ilan Bar-on
I. BarOn , B. Codenotti, and M. Leoncini presented a linear time algorithm for checking the nonsingularity of general tridiagonal matrices BIT, 36:206, 19966. A detailed implementation of their algorithm, with some extensions to possibly reducible matrices, is further described in the present paper.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1966
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1966.17.211