On real symmetric determinants whose principal diagonal elements are zero
نویسندگان
چکیده
منابع مشابه
Determinants Whose Elements Have Equal Norm1
Hence A, B, C equal A', B', C in some order. Each of the 6 orders leads immediately to the proportionality of two rows or columns. The above theorem, in its specialization to minors of Vandermonde determinants composed of gth roots of unity in R*, was used in [l] for the proof of a theorem on power series without terms whose subscript belongs to one of 3 residue classes modulo an arbitrary inte...
متن کاملPrimitive Zero-Symmetric Sign Pattern Matrices with Zero Diagonal Attaining the Maximum Base
A sign pattern matrix or sign pattern A is a matrix whose entries are from the set {1,−1, 0}. Notice that for a square sign pattern matrixA, in the computation of the signs of the entries of the power A, an ambiguous sign may arise when a positive sign is added to a negative sign. So a new symbol # was introduced in 1 to denote such an ambiguous sign. The powers of a square sign pattern have be...
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 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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We give a complexity-theoretic characterization of the class of problems in NP having zeroknowledge argument systems. This characterization is symmetric in its treatment of the zero knowledge and the soundness conditions, and thus we deduce that the class of problems in NP ∩ coNP having zero-knowledge arguments is closed under complement. Furthermore, we show that a problem in NP has a statisti...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1932
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1932-05366-6