Sentence examples for matrix with rank from inspiring English sources

The identity matrix with rank b is denoted by I b.

It is easy to find that the composite matrix is also a full column rank matrix with rank.

The channel matrix H is a matrix with rank r and with positive eigenvalues of H H H generally denoted by λ k, k=1,2,…,r.

From (18) and (19), it is easy to see that since α i  ≠ α j, (i ≠ j), A is a full column rank matrix with rank (A = M. Similarly, since β i  ≠ β j, (i ≠ j), Ψ is a full-rank diagonal matrix with rank  = M.

Considering ({{mathbf {T}}^ bot } = {mathbf {I}} - {{mathbf {h}}_{RP}}left ({{mathbf {h}}_{RP}^{H}{{mathbf {h}}_{RP}}} right){mathbf {h}}_{RP}^{H}) is the projection idempotent matrix with rank (M−1), (T ⊥) H T ⊥ is a Hermitian matrix with rank (M−1).

By applying a standard Lagrangian multiplier method, the optimal weight vector is given as w ZF =T ⊥ h RD /∥T ⊥ h RD ∥, where ({{mathbf {T}}^ bot } = {mathbf {I}} - {{mathbf {h}}_{RP}}left ({{mathbf {h}}_{RP}^{H}{{mathbf {h}}_{RP}}} right){mathbf {h}}_{RP}^{H}) is the projection idempotent matrix with rank (M−1).

The new method can be applied for rectangular matrix with full-rank and square matrix with rank-deficient only.

We find sometimes that the background is exactly a rank-one matrix, instead of a general low-rank matrix, so Li et al. [ 16] proposed to replace low-rank matrix with rank-one matrix which avoids any SVD completely.

The achievable rate of chunked codes for transfer matrices with rank distribution t=(t 0,t 1,…,t m ) is upper bounded by (bar {t}/m), where bar{t}=mathrm{E}[!text{rk}(mathbf{T}_{j})]=sum_{i=1}^{m} {it}_{i}.

Except for pathological setups exhibiting full spatial correlation between pairs of transmit or receive antennas (scenario not considered in this analysis), Ʀ TX and Ʀ RX are full rank matrices with rank Ʀ TX = N T and rank Ʀ RX = N R, and therefore, rank R g min = N T N R rank Ʀ h g min. (51).

where the first step follows by the invertibility of A. For any s and r such that s≥r, denote the event M j =s and rk(S j )=r by (mathcal {E}_{s,r}), and define (mathcal {S}_{s,r}) to be the set of all m×s matrices with rank r.