Correction to ‘‘On matrices whose real linear combinations are nonsingular”
نویسندگان
چکیده
منابع مشابه
Correction 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...
متن کاملOn 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 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.
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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) ...
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The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1966
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1966-0201460-1