Sentence examples for matrices of rank from inspiring English sources

Thus, A is the sum of two matrices of rank 1 and, hence, at most of rank 2.

Notice that T x T x H and Ξ x Ξ x H are two orthogonal projection matrices of rank P and M−P, respectively.

We propose to use the spectral matrices of rank one (linked to each th source) obtained from the decomposition of the multicomponent wideband spectral matrix (see (15)).

The set of 2 × 2 symmetric positive semidefinite matrices of rank one will be noted S + ( 1, 2 ) throughout the paper (see [16] for a complete study of the set S + ( p, n ) of n × n symmetric positive semidefinite matrices of fixed-rank p < n ).

Since the number of subcarriers allocated to each user is variable, and the number of users having partially overlapping transmission bandwidths with one another may be more than 2, the receiver must be dimensioned for the worst-case scenario and should be able to invert matrices of rank hundreds or thousands.

Let (U_{2}) and V contain exactly one non-zero element such that the non-zero element in (U_{2}) is in a different column to the non-zero element in V. Let W=J_{2}+U_{2}^V-V^U_{2}. (4.6) Then (U_{2}^V) and (V^U_{2}) are (8times8) matrices of rank 1, (U_{2}^V-V^U_{2}) is an (8times8) matrix of rank 2 and W is an (8times8) matrix of rank at least 6.

Similarly, the matrices that correspond to SCEN3 and SCEN5 behave like matrices of ranks 2 and 3, respectively.

Now it is clear that there are diagonally magic matrices of ranks 0, 1, 2. Indeed, (operatorname{rank} (0_{ntimes n} )=0), (operatorname{rank} ([1]_{ntimes n} )=1), and (operatorname{rank}(B_{n})=operatorname{rank}(C_{n})=2).

Letting, should be a positive semidefinite matrix of rank.

I N Identity matrix of rank N. T, H Transpose and Hermitian transpose.

Let A be an (mtimes n) real (complex) matrix of rank r.