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The warning about over-actuated systems is given because the input/output rectangular matrix transformations needed in this case may assume a rigid platform.
Mathai, Jacobians of Matrix Transformations and Functions of Matrix Arguments, World Scientific, 1997.
Many authors have extensively developed the theory of the matrix transformations between some sequence spaces; we refer the reader to [1-6].
Two notions--one of [sigma]-mean and the other of de la Vallee-Pousin mean--play a very active role in recent research on matrix transformations.
1, it is formed a homogeneous matrix transformations.
The notion of regularity for two dimensional matrix transformations was presented by Silverman [40] and Toeplitz [41].
Characterisations of classes of matrix transformations between sequence spaces constitute a wide, interesting and important field in both summability and operator theory.
The Silverman-Toeplitz theorem [15], [16], characterizes the regularity of two dimensional matrix transformations.
Specific topics include a survey of Kalton's work, twisted dualities in Banach space theory, complexity and homogeneity in Banach spaces, conditions for stochastic integrability in UMD Banach spaces, a new infinite game for Banach spaces with applications, greedy approximation in Banach spaces, Kolmogorov numbers of matrix transformations, a general Baker super-stability criterion for the D'Alembert functional equation, aspects of probabilistic Littlewood-Paley theory, properties related to the Dauavet property, perturbations of ideal complements and asymptotically transitive Banach spaces.
Keywords: Time scales, function spaces, duals, matrix transformations.
Matrix transformation involving [chi] were characterized by Sridhar [20] and Sirajiudeen [21].