• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1273-1283
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• 2019

In matrix analysis, the Wielandt-Mirsky conjecture states that $$dist({\sigma}(A),{\sigma}(B)){\leq}{\parallel}A-B{\parallel}$$ for any normal matrices $A,B{\in}{\mathbb{C}}^{n{\times}n}$ and any operator norm ${\parallel}{\cdot}{\parallel}$ on $C^{n{\times}n}$. Here dist(${\sigma}(A),{\sigma}(B)$) denotes the optimal matching distance between the spectra of the matrices A and B. It was proved by A. J. Holbrook (1992) that this conjecture is false in general. However it is true for the Frobenius distance and the Frobenius norm (the Hoffman-Wielandt inequality). The main aim of this paper is to study the Hoffman-Wielandt inequality and some weaker versions of the Wielandt-Mirsky conjecture for matrix polynomials.

• The Journal of the Korea Contents Association
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• v.19 no.1
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• pp.125-131
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• 2019

A vanishing point is a point on an image to which parallel lines projected from a real space gather. A vanishing point in a road space provides important spatial information. It is possible to improve the position of an extracted lane or generate a depth map image using a vanishing point in the road space. In this paper, we propose a method of detecting vanishing points on images taken from a vehicle's point of view using Deep Neural Network (DNN) and Histogram of Oriented Gradient (HoG). The proposed algorithm is divided into a HoG feature extraction step, in which the edge direction is extracted by dividing an image into blocks, a DNN learning step, and a test step. In the learning stage, learning is performed using 2,300 road images taken from a vehicle's point of views. In the test phase, the efficiency of the proposed algorithm using the Normalized Euclidean Distance (NormDist) method is measured.