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We assume that B has full rank, i.e., rank(B)= m.
Furthermore, when k="1 (Schröder's equation), necessary and sufficient conditions on ϕ are given to ensure F has full rank near 0 without the added assumption of diagonalizability as needed in the 2003 Cowen/MacCluer paper.
Suppose that F ′ ( x ∗ ) has full rank.
provided that the has full rank.
Since has full rank, for all.
If r=K, the channel has full rank.
which has full rank but is not necessarily orthogonal.
When (mathbf {X}) has full rank, there is a unique solution for (kappa _i).
Lemma 3.1 Suppose F ( x ∗ ) = 0, and F ′ ( x ∗ ) has full rank.
Assumptions guarantee that the virtual MIMO channel matrix in (7) has full rank with high probability.
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A regularization term α is added above since in practice, will not have full rank.
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