Sentence examples for minus orders from inspiring English sources

It is easy to verify that, for a full column rank matrix C with proper size, the minus orders A ≤ ̄ B and C A ≤ ̄ C B are equivalent, but if C is not a full column rank matrix, this implication may be not true.

Several equivalent conditions for the minus ordering are established.

A similar consequence on the minus ordering is established as below.

Special attention is paid to the star ordering of a sum of two matrices and the minus ordering of matrix product.

Theorem 7 Let A, C ∈ C m×n, and B, D ∈ C m×k be minus ordered as A ≤ ̄ C, B ≤ ̄ D. If R(C) ∩ R(D) = {0}, then A B ≤ ̄ C D. Proof.

hence, A B ≤ ̄ C D. The following statement can be deduced from Lemma 3. Theorem 8 Let A, C ∈ C m×n be minus ordered as A ≤ ̄ C, and B, D ∈ C m×k.

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Therefore, we perform additional simulations varying the fluid input from depth by plus or minus one order of magnitude at t = 0 (Fig. 14).

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The second partial ordering of interest is minus (rank subtractivity) ordering devised by Hartwig [4] and independently by Nambooripad [5].

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