Sentence examples for unitary norm from inspiring English sources

Denote as a secret vector in the secret subspace, with unitary norm.

Bhatia and Davis [5] extended inequality (1) to the matrix case, they showed that it holds for positive semi-definite matrices, in the following form: bigl|!bigl|!bigl|A^{frac{1}{2}}bigr|ac{1}{2}}bigr|lebigl|bigl|lebigl|H_{nu}!bigl|H_{nu}(A, B bigr|!bigr|!bigr|lebiggl|!biggl|!biggl|frac{A+B}{2}biggr|!biggr|!biggr|, (9) where (|!|!|cdot|!|!|) is any invariant unitary norm.

After each learning step, the provisional W ~ i j t weights are normalized into unitary norm: (8) ∑ j   W i j t 2 = 1.

Their norm equals one, they are independent and we assume that they are orthogonal since their cross correlations are negligible (their expectations are zero, and their standard deviations equal ) compared to their unitary norms when is big.

We say a function ⦀ ⋅ ⦀ : B ( H ) → R is a unitary invariant norm (or symmetric norm) if it is a norm satisfying the invariance property ⦀ u x v ⦀ = ⦀ x ⦀ for all x and all unitary operators u and v in B ( H ). In this paper, we consider the noncommutative L p spaces of τ-measurable operators affiliated with a semi-finite von Neumann algebra equipped with a normal faithful semi-finite trace τ.

The following lemma has been shown in [16], and it is considered as a refined matrix Young inequality for every unitary invariant norm.

Through the following, we would like to obtain upper bound for (vert !vert !vert AXB^ vert !vert !vert ), for every unitary invariant norm.

This is the Hölder inequality of unitary invariant norms for matrices.

We prove that a unital purely infinite simple C*-algebra has C*-exponential rank at most 1 + ϵ, and therefore has the property weak (FU): Every element of the identity component of the unitary group is norm limit of unitaries with finite spectrum.

This is due to the fact that the DCT matrix is unitary and preservesℓ2-norm of the data.

Since Q is unitary, it preserves Euclidean norm as well as noise statistics.