Wang, "
Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations," Computers & Mathematics with Applications, vol.
This resonant particle (see Figure 4) is
bisymmetric, exhibiting an electric wall and a magnetic wall at the fundamental resonance.
The general coupled matrix equations over generalized
bisymmetric matrices.
The solutions X to the linear matrix equation with special structures have been widely studied, for example, symmetric solutions (see [1-5]), R-symmetric solutions (see [6]), (R, S)-symmetric solutions (see [7, 8]),
bisymmetric solutions (see [9-12]), centrosymmetric solutions (see [13]), and other general solutions (see [14-23]).
Hence substituting [R.sup.(-q)] = - [R.sup.(q)], [Z.sub.-n] = [Z.sub.n] and [[??].sub.-q(B)] = [[??].sub.q(B)] in the matrix of (31) leads to a
bisymmetric matrix.
Hajarian, On the generalized
bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations, Linear and Multilinear Algebra, 59 (2011) 1281-1309.
Majumdar [1] gave the formula for n-th term of the following sequences: Smarandache cyclic natural determinant sequence, Smarandache cyclic arithmetic determinant sequence, Smarandache
bisymmetric natural determinant sequence and Smarandache
bisymmetric arithmetic determinant sequence.
[1.] Gilbert, B., "The MICRO-MIXER: A highly linear variant of the Gilbert mixer using a
bisymmetric Class-AB input stage," IEEE Journal of Solid-State Circuits, Vol.
A matrix X = ([x.sub.ij]) [member of] [R.sub.nxn] is said to be
bisymmetric if [x.sub.ij] = [x.sub.ji] = [x.sub.n-i+1,n-j+1] for all 1 [less than or equal to] i,j [less than or equal to] n.
By extending the idea of conjugate gradient method, Dehghan and Hajarian [12] constructed an iterative algorithm to solve (1) with q = p over generalized
bisymmetric matrices.
In [1], Murthy introduced the concept of the Smarandache Cyclic Determinant Natural Sequence, the Smarandache Cyclic Arithmetic Determinant Sequence, the Smarandache
Bisymmetric Determinant Natural Sequence, and the Smarandache
Bisymmetric Arithmetic Determinant Sequence.
Dehghan and Hajarian constructed finite iterative algorithms to solve several linear matrix equations over (anti)reflexive [22-24], generalized centrosymmetric [25, 26], and generalized
bisymmetric [27, 28] matrices.