Let μ i denote a diagonal matrix of eigenvalues and p i denote the matrix with corresponding eigenvectors of the discrete transition matrix at frequency i∈{m,q}.
According to Theorem 3.2, there exists an invertible matrix H, such that J=H^{-1}hat{E}^{d}hat{A}H= operatorname{diag}(J_{1}, J_{2}, ldots, J_{r}, mathbf{0}), (24) where (J_{i}), is a Jordan canonical form, (1leq i leq r), and 0 is a zero matrix with corresponding dimension.
Then there exists an invertible matrix H such that H^{-1}hat{E}^{d}hat{A}H=operatorname{diag}(J_{1},J_{2}, ldots, J_{r},mathbf{0}), (21) where (J_{i}, 1leq i leq r), are Jordan canonical forms and 0 is a zero matrix with corresponding dimension.
It is worth pointing out that the total computational complexity of CA is related with the iteration number, the size of S. In particular, each iteration requires to handle a singular value decomposition (SVD) of N T ×M dimension matrix with corresponding to computational complexity (O(M{N^{2}_{T}}+{N^{3}_{T}}))[24].
Otherwise, g usually is a rectangular zero-one matrix with corresponding rows deleted (represent the immeasurable states) from the identity matrix I n.
The data sets are represented as matrices with rows corresponding to patients and columns corresponding to genes, proteins, or CNVs.
For given genes l, m∈{1,..., G}, such that l≠ m, consider the genotype matrices,,, and, with corresponding reduced kernel representations,,, and.
The uncertain communication topology is modelled by a finite number of Laplacian matrices with their corresponding scheduling functions.
The NASTRAN computer code is utilized to find theoretical mass and stiffness matrices with their corresponding natural frequencies and mode shapes.
A recent study has shown that single cell populations (SCPs) derived from MDA-MB-231 cells exhibited increased proliferation and migration when seeded on matrices with rigidities corresponding to the native rigidities of the organs where metastasis was observed [30].
