相关论文: A Determinantal Inequality for the Geometric Mean …

We present some new inequalities related to determinant and trace for positive semidefinite block matrices by using symmetric tensor product, which are extensions of Fiedler-Markham's inequality and Thompson's inequality.

In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath [13] in a more general setting and also relate to recent work of…

Compared to the error diffusion, dot diffusion provides an additional pixel-level parallelism for digital halftoning. However, even though its periodic and blocking artifacts had been eased by previous works, it was still far from…

Diffusion tensor imaging (DTI) is a popular magnetic resonance imaging technique used to characterize microstructural changes in the brain. DTI studies quantify the diffusion of water molecules in a voxel using an estimated 3x3 symmetric…

We introduce two equations expressing the inverse determinant of a full rank matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ in terms of expectations over matrix-vector products. The first relationship is $|\mathrm{det} (\mathbf{A})|^{-1} =…

In this paper we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting,…

We derive an identity for the determinant of the sum of two $n\times n$ matrices, $A$ and $B$, whose entries are defined via contour integrals. Specifically, we consider $A(i,j)=\frac{1}{2\pi\mathrm{i}}\oint_0…

In this paper we introduce the limit, unique solution of the nonlinear equations, geodesic property, tolerance relations and pinch on the spectral geometric mean for two positive definite operators. We show that the spectral geometric mean…

Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.

A hypersurface $H$ in $\mathbb{P}^r$ of degree $n$ is called determinantal if it is the zero locus of a polynomial of the form $\operatorname{det}(x_0 A_0 + \ldots + x_r A_r)$ for some $(r+1)$-tuple of $n \times n$ matrices $A = (A_0,…

The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation…

The concept of Loewner (partial) order for general complex matrices is introduced. After giving the definition of arithmetic, geometric, and harmonic mean for accretive-dissipative matrices, we study their basic properties. An AM-GM-HM…

In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…

For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…

This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures…

The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping…

There are various generalizations of the geometric mean $(a,b)\mapsto a^{1/2}b^{1/2}$ for $a,b\in \mathbb{R}^+$ to positive matrices, and we consider the standard positive geometric mean $(X,Y)\mapsto…

Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…

We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…

In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.