diagonal matrix


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diagonal matrix

[dī′ag·ən·əl ′mā·triks]
(mathematics)
A matrix whose nonzero entries all lie on the principal diagonal.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
where [D.sup.(r).sub.1] is a diagonal matrix in which the diagonal elements are [d1.sup.(r).sub.jj] = 1/[(2[parallel][P.sup.(r).sub.i][parallel]).sup.q], [D.sup.(r).sub.2] is a diagonal matrix in which the diagonal elements are [d2.sup.(r).sub.jj] = 1/[(2[parallel][([P.sup.(r)T][Z.sup.(r)[H.sub.n] - [Y.sup.(r)][H.sub.n]).sub.i][parallel]).sup.q].
where [and] is a diagonal matrix which can be adjusted to satisfy the hybrid precoding power constraints as [mathematical expression not reproducible].
So, H is a quasidiagonal matrix and so is [PSI], since [beta] is a diagonal matrix.
Based on the decoupling principle for a unit diagonal matrix, (3) can be written as
where [K.sub.2] [member of] [R.sup.3x3] is the designed positive definite diagonal matrix and [mathematical expression not reproducible]; is the positive constant.
where [k.sub.2] [member of] [R.sup.3x3] is a diagonal matrix and each diagonal element of the matrix is a positive constant.
The diagonal matrix [D.sup.p] of the penalty graph [G.sub.p] is defined as
where [H.sub.1] is a diagonal matrix consisting of the channel transfer functions at all the N subcarriers of one OFDM symbol, [phi] and [beta] denote N x 1 vectors consisting of the time-domain Tx PN and Rx PN of one OFDM symbol, respectively, F denotes an N x N unitary discrete Fourier transform (DFT) matrix, whose elements are given by exp(-j2[pi]kl/N)/[square root of N] (k, l = 0, ..., N - 1), and [w.sub.1] is an N x 1 AWGN vector.
Given a basic partitions set n, let the corresponding coassociation matrix be C, the diagonal matrix whose diagonal elements are sums of rows of C be D1, and the diagonal element set of D1 be {[w.sub.b(a)]}.
where [S.sub.1] is a positive diagonal matrix. It is possible to rewrite (17) as
where [x.sub.i] (t) = [([x.sub.i1] (t), [x.sub.i2] (t), ..., [x.sub.in] (t)).sup.T] [member of] [R.sup.n] is the ith node state variable, f : [R.sup.n] [right arrow] [R.sup.n] and g : [R.sup.n] [right arrow] [R.sup.n] are differentiable vector function, [alpha] [member of] [R.sup.l] is unknown parameter vector, [tau] is time delay, r is coupled matrix, [GAMMA] = diag{[[gamma].sub.1], [[gamma].sub.2], ..., [[gamma].sub.n]) is diagonal matrix and [parallel][??][parallel] > 0, C = [([c.sub.ij]).sub.NxN] is external coupled matrix, [c.sub.ij] is defined as : [c.sub.ij] > 0 if there is a connection between node i and node j, otherwise [c.sub.ij] = [c.sub.ji] = 0, and the diagonal elements [c.sub.ij] is defined as
Using the obtained values [a.sub.i,j], [b.sub.i,j], i,j = [bar.1,N] we can determine the 3-diagonal N-order matrices [A.sup.e.sub.z], [B.sup.e.sub.z] with these elements, the N-order diagonal matrix B0 with the elements [[b.sub.10], 0,0, ...