Sentence examples for a matrix norm from inspiring English sources
and therefore there exists a matrix norm on such that (4.10).
This norm on is a matrix norm, called the matrix norm induced by.
A matrix norm on is called an induced matrix norm if it is induced by some norm on.
Assume that and that for every eigenvalue of with modulus, that is, is nonexpansive relative to a matrix norm.
If is a matrix norm on, there exists an induced matrix norm on such that for all (cf. [1, page 297]).
The condition obtained for the robust stability establishes a matrix-norm relationship between the network parameters of the neural system, and therefore it can easily be verified.
For (1 leq p leq2), it is well known [2] that the scalar function (1.1) of a matrix A is a submultiplicative matrix norm.
A matrix normed space ( X, { ∥ ⋅ ∥ n } ) is called an L ∞ -matrix normed space if ∥ x ⊕ y ∥ n + k = max { ∥ x ∥ n, ∥ y ∥ k } holds for all x ∈ M n ( X ) and all y ∈ M k ( X ).
It is also supposed that, for a given control law strategy, these performance specifications can always be expressed in terms of an and/or a transfer matrix norm of the corresponding channel, namely,, where the matrices and are set to select the desired input/output channel from the system closed-loop transfer matrix.
Basic properties of matricially normed spaces are considered, and a simple matrix norm characterization of the subspaces of C∗-algebras is given.
