Precomposing by L or (theta _{i}) does not change the norm of a vector (each component being multiplied by a complex number on the unit circle).
A matrix pencil is a family of matrices s F − G, parametrized by a complex number s, see [39, 41, 44, 45].
With respect to ordinary operations of addition and multiplication by a complex number, ({mathscr {K}}_{vec{x}} ) is a Banach space.
In conventional OBF [17], at time slot t, the same block of symbols x t) is multiplied by a complex number α n ( t ) exp ( j ϕ n ( t ) ) at antenna n and transmitted, respectively, from all the antennas, for n = 1,…,N, such that ∑ n = 1 N α n ( t ) = 1, preserving the total transmit power.
The health of individuals and populations is not determined by any one factor, but by a complex number of factors that interact with each other.
We denote the set of functions by, where is a complex number and is as stated in (1.12).
For 0 ≤ ξ ≤ L, on the other hand, the solution is represented by, where k is a complex number and, by assumption, the expression under the square root is now negative.
It builds a complex number by taking the centroid distance r(t) := |(x t),y(t)) - (x 0,y 0)| (see Equation (14)) as real part and the distance d(t) as imaginary part.
