منابع مشابه
A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices
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 ...
متن کاملInverse Young inequality in quaternion matrices
Inverse Young inequality asserts that if $nu >1$, then $|zw|ge nu|z|^{frac{1}{nu}}+(1-nu)|w|^{frac{1}{1-nu}}$, for all complex numbers $z$ and $w$, and equality holds if and only if $|z|^{frac{1}{nu}}=|w|^{frac{1}{1-nu}}$. In this paper the complex representation of quaternion matrices is applied to establish the inverse Young inequality for matrices of quaternions. Moreover, a necessary and ...
متن کاملA Non-commutative Cryptosystem Based on Quaternion Algebras
We propose BQTRU, a non-commutative NTRU-like cryptosystem over quaternion algebras. This cryptosystem uses bivariate polynomials as the underling ring. The multiplication operation in our cryptosystem can be performed with high speed using quaternions algebras over finite rings. As a consequence, the key generation and encryption process of our cryptosystem is faster than NTRU in comparable pa...
متن کاملQuo Vadis Quaternion? Cryptanalysis of Rainbow over Non-commutative Rings
The Rainbow Signature Scheme is a non-trivial generalization of the well known Unbalanced Oil and Vinegar Signature Scheme (Eurocrypt '99) minimizing the length of the signatures. Recently a new variant based on non-commutative rings, called NC-Rainbow, was introduced at CT-RSA 2012 to further minimize the secret key size. We disprove the claim that NC-Rainbow is as secure as Rainbow in general...
متن کاملNon-commutative standard polynomials applied to matrices
The Amitsur–Levitski Theorem tells us that the standard polynomial in 2n non-commuting indeterminates vanishes identically over the matrix algebra Mn(K). For K = R or C and 2≤ r ≤ 2n−1, we investigate how big Sr(A1, . . . ,Ar) can be when A1, . . . ,Ar belong to the unit ball. We privilegiate the Frobenius norm, for which the case r = 2 was solved recently by several authors. Our main result is...
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ژورنال
عنوان ژورنال: Advances in Applied Clifford Algebras
سال: 2014
ISSN: 0188-7009,1661-4909
DOI: 10.1007/s00006-014-0449-1