Given an m×n matrix A and an n×p matrix B, it holds that [25] rank ( A ) + rank ( B ) − n ≤ rank ( A B ) ≤ min rank ( A ), rank ( B ). (55).
According to the rank theorem in matrix theory, dim [ Null ( A ) ] = n - rank ( A ), (13).
On the other hand, if α i ⊗ b j are linearly independent, then all the column vectors of A ⊗ B are linearly independent, and the matrix rank of A ⊗ B is nq = Rank (A ⊗ B) = Rank A × Rank B. Finally, we can deduce that: Rank A = n, Rank B = q, which means (α1, α2,⋯,α n ) and (b1,b2,⋯,b q ) are linearly independent.
"You rank a quarterback by championships.
This gives each rank a smooth, parabolic look.
With only 55 points, the Rangers rank a sorry 25th among the 30 teams.
The highest rank a Boy Scout can achieve is Eagle Scout.
At Mr. Peguero's store, computer repairs rank a distant second to the two-way radio business.
It is therefore easy to rank a collection of images by their entropy.
It is also asking the authors of recommendation letters to rank a candidate's integrity on a five-point scale.
Below cabinet rank a raft of women were promoted, but not quite to the extent that some advance briefing suggested.
