However, for the simulated datasets, the average ranking and minimal ranking methods were outperformed by In and FST, but their performance were either better or very similar to the most commonly used method Delta, FIC and SIC (Additional file 11, Table S5 and Additional file 12, Table S6).
Minimizing the regression objective function in Eq. 4 yields W matrices of minimal rank for each task.
Some previous systematical researches on maximal and minimal ranks of matrix expressions or partial matrices and their applications can be found in [17 20].
In fact, maximal and minimal ranks of matrix expressions or partial matrices have been the main objects of study in matrix theory and applications.
We give in this article the maximal and minimal ranks of the matrix expression A-B1V1C1-B2V2C2-B3V3C3-B4V4C4 with respect to V1, V2, V3, and V4.
In recent years, the present author reconsidered the maximal and minimal ranks of matrix expressions or partial matrices by using some tricky operations on block matrices and generalized inverses of matrices, and obtained many new formulas for maximal and minimal ranks of matrix expressions or partial matrices and their applications, see [4, 6, 9, 21 28].
This paper first deals with bracing of this minimal rank, connecting to the least number of freedoms possible, and later generalises this to higher rank bracing, with connections to any number of freedoms.
This paper presents a new controller degree bound for the H∞ control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region.
Knowledge of the cardinality and the number of minimal rank reducing observation sets in experimental design is important information which makes a useful contribution to the statistician's tool-kit to assist in the selection of incomplete block designs.
On the other hand, from (39) and Theorems 2.5 and 3.3, we can easily obtain the minimal rank of the partial matrix (A BM 1)C DN(1 G) with respect to M 1) ∈ M{1} and N(1) ∈ N{1}.
Because the rank of matrix is an integer between 0 and the minimal of row and column numbers of the matrix, maximal and minimal ranks of partial matrix or matrix expressions must exist with respect to their variant entries or variant matrices.
