On matrices whose nontrivial real linear combinations are nonsingular.
نویسندگان
چکیده
منابع مشابه
On Matrices Whose Real Linear Combinations Are Nonsingular
Let A be either the real field R, or the complex field C, or the skew field Q of quaternions. Let Au A2, • ■ ■ , Ak be nXn matrices with entries from A. Consider a typical linear combination E"-iV^> with real coefficients Xy; we shall say that the set {A¡} "has the property P" if such a linear combination is nonsingular (invertible) except when all the coefficients X> are zero. We shall write A...
متن کاملCorrection to "on Matrices Whose Real Linear Combinations Are Nonsingular"
2. -, Rings with a pivotal monomial, Proc. Amer. Math. Soc. 9 (1958), 635642. 3. L. P. Belluce and S. K. Jain, Prime rings having a one-sided ideal satisfying a polynomial identity, Abstract 614-89, Notices Amer. Math. Soc. 11 (1964), p. 554. 4. N. Jacobson, Structure of rings, Amer. Math. Soc. Colloq. Publ. Vol. 37, Amer. Math. Soc, Providence, R. I., 1956. 5. I. Kaplansky, Rings with a polyno...
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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.
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Let e and n be positive integers and S = {x1, . . . , xn} be a set of n distinct positive integers. The n × n matrix having eth power [xi, xj ] of the least common multiple of xi and xj as its (i, j)-entry is called the eth power least common multiple (LCM) matrix on S, denoted by ([S]). The set S is said to be gcd closed (respectively, lcm closed) if (xi, xj) ∈ S (respectively, [xi, xj ] ∈ S) ...
متن کاملMatrices A such that AA+ - A+A are nonsingular
In this paper we study the class of square matrices A such that AA − AA is nonsingular, where A stands for the Moore–Penrose inverse of A. Among several characterizations we prove that for a matrix A of order n, the difference AA−AA is nonsingular if and only if R(A) ⊕ R(A) = Cn,1, where R(·) denotes the range space. Also we study matrices A such that R(A) = R(A).
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0274478-2