Short Normal Paths and Spectral Variation1
نویسندگان
چکیده
We introduce the notion of a "short normal path" between matrices S and T, that is, a continuous path from S to T consisting of normal matrices and having the same length as the straight line path from S to T. By this means we prove that for certain normal matrices S and T the eigenvalues of S and T may be paired in such a way that the maximum distance (in the complex plane) between the pairs is no more than the operator norm ||S T\\. In particular, we generalize and provide a new approach to a recent result of Bhatia and Davis treating the case of unitary 5 and T.
منابع مشابه
Detecting buried channels using linear least square RGB color stacking method based on deconvolutive short time Fourier transform
Buried channels are one of the stratigraphic hydrocarbon traps. They are often filled with a variety of porous and permeable sediments so they are important in the exploration of oil and gas reservoirs. In reflection seismic data, high-frequency components are sensitive to the channel thickness, whereas, low-frequency components are sensitive to the channel infill materials. Therefore, decompos...
متن کاملOn spectral radius of strongly connected digraphs
It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.
متن کاملOn the Remarkable Formula for Spectral Distance of Block Southeast Submatrix
This paper presents a remarkable formula for spectral distance of a given block normal matrix $G_{D_0} = begin{pmatrix} A & B \ C & D_0 end{pmatrix} $ to set of block normal matrix $G_{D}$ (as same as $G_{D_0}$ except block $D$ which is replaced by block $D_0$), in which $A in mathbb{C}^{ntimes n}$ is invertible, $ B in mathbb{C}^{ntimes m}, C in mathbb{C}^{mti...
متن کاملTechnical guide to Set Up a Spectral Solar Direct Normal Irradiance Permanent Station: Study Area- Hannover, Germany
The spectral Direct Normal Irradiance (SDNI) is a basic radiometric quantity from which many other quantities can be derived. It provides not only information about the spectral and distribution of the direct solar radiation reaching a particular location. Accurate knowledge about the spectral direct irradiance shall enable us to gain new scientific results in the: determination of cloud effect...
متن کاملCommon Raman Spectral Markers among Different Tissues for Cancer Detection
Introduction Raman spectroscopy is a vibrational spectroscopic technique, based on inelastic scattering of monochromatic light. This technique can provide valuable information about biomolecular changes, associated with neoplastic transformation. The purpose of this study was to find Raman spectral markers for distinguishing normal samples from cancerous ones in different tissues. Materials and...
متن کامل