Sentence examples for matrix decomposition theorem from inspiring English sources

Finally, an optimal solution can be found by using the Charnes-Cooper transformation and the rank-one matrix decomposition theorem.

We exploit the Charnes-Cooper variable transformation and a specific rank-one matrix decomposition theorem [25], which is cited as the following lemma.

A nonconvex formulation for such optimization problem can be solved using SDR technique, Charnes-Cooper transformation, and rank-one matrix decomposition theorem.

Finally, a global optimal solution can be found by using the Charnes-Cooper transformation and the rank-one matrix decomposition theorem [19, 20].

Here we propose an optimal solution by using the idea of Charnes-Cooper transformation and the rank-one matrix decomposition theorem.

Since A and B are positive matrices, by the spectral decomposition theorem, there exist unitary matrices (U,V in M_{n}) satisfying (A = ULambda _{1}U^), (B = VLambda_{2}V^), where (Lambda_{1} = operatorname{diag} ( lambda_{1},ldotsa_{2},lambda_{nmbda_{n} )), (Lambda_{2} = operatorname{diag} ( mu_{1},mu_{2}, ldots,mu_{n} )) ((lambda_{i} ge0), (mu_{i} ge0), (i = 1,2,ldots,n)).

Before proving Theorem 2, we need the following Lemma: [27] Consider a matrix decomposition X= A B T, where A ∈ ℂ I × F is a Vandermonde matrix with distinct nonzero generator and B ∈ ℂ J × F is a 'tall' or 'square' matrix with full column rank.

Theorem 2.9 (Decomposition theorem).

(Decomposition theorem of time scales).

[10] (Generalized orthogonal decomposition theorem).

which is just Riesz orthogonal decomposition theorem.