نتایج جستجو برای: quaternion matrices and linear algebra
تعداد نتایج: 16911737 فیلتر نتایج به سال:
A general method is presented for establishing universal factorization equalities for 2×2 and 4×4 block matrices. As applications, some universal factorization equalities for matrices over four-dimensional algebras are established, in particular, over the Hamiltonian quaternion algebra.
A general method is presented for establishing universal factorization equalities for 2×2 and 4×4 block matrices. As applications, some universal factorization equalities for matrices over four-dimensional algebras are established, in particular, over the Hamiltonian quaternion algebra.
assume ? ? l2(rd) has fourier transform continuous at the origin, with ˆ ?(0) = 1, and thatcan be represented by an affine series f = j>0 k?zd c j,k?j,k for some coefficients satisfying c 1(2) = j>0 k?zd |c j,k|2 1/2 <?. here ?j,k(x) = |deta j |1/2?(a jx ?k) and the dilation matrices a j expand, for example a j = 2j i. the result improves an observation by daubechies that t...
In this chapter, the problem of quaternion beamformer based on linear and widely linear hypercomplex processing is investigated in scenarios, where there exist one signal and one interference that are uncorrelated. First, we introduce brief information about the quaternion algebra and a quaternion model of linear symmetric array with twocomponent electromagnetic (EM) vector-sensors is presented...
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex quaternion matrices, and so on. AMS Mathematics Subject Classification: 15A06; 15A24; 15A33
An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R.
in this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. our results are similar to some inequalities shown by bhatia and kittaneh in [linear algebra appl. 308 (2000) 203-211] and [linear algebra appl. 428 (2008) 2177-2191].
Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the noncommutative...
we commence by using from a new norm on l1(g) the -algebra of all integrable functions on locally compact group g, to make the c-algebra c(g). consequently, we find its dual b(g), which is a banach algebra so-called fourier-stieltjes algebra, in the set of all continuous functions on g. we consider most of important basic theorems about this algebra. this consideration leads to a rather com...
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