Sentence examples for a matrix version from inspiring English sources
Furthermore, we provide a matrix version.
This is a matrix version of (1.1).
This is a matrix version of the inequality (1.4).
It is a matrix version of the arithmetic-geometric mean inequality.
Remark 2.3 As an application of Theorem 2.2, we now present a matrix version of (1.3).
Moreover, we will obtain a matrix version of the Heinz inequality for the Hilbert-Schmidt norm.
A well-know matrix version of Kantorovich inequality asserts that (see[1 3]).
As a result, the matrix version of equation (5) is: y = ρWy + βX + ε (6).
Denote by λ 1 ≤ λ 2 ≤ ⋯ ≤ λ n the eigenvalues of an Hermitian matrix A. The matrix version of the well-known Kantorovich inequality for a positive definite matrix A is stated as follows (see, e.g., [1, 2]): 1 ≤ x ∗ A x x ∗ A − 1 x ( x ∗ x ) 2 ≤ ( λ 1 + λ n ) 2 4 λ 1 λ n (1.1).
A further improvement of the matrix version of (1.3) is proposed in [8], where the classical Kantorovich inequality (1.1) is modified to apply not only to positive definite, but also to all invertible Hermitian matrices.
The difference is that we present Young's inequalities in four more precise intervals of ([0,1]) other than two sections of ([0,1]), and also the operator form and the matrix version get a promotion.
