Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...

‎‎‎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...

Let G be a finite connected graph. If x and y are vertices of G, one may define a distance function d, on G by letting d&x, y) be the minimal length of any path between x and y in G (with d&, x) = 0). Thus, for example, d&x, y) = 1 if and only if {x, y} is an edge of G. Furthermore, we define the distance matrix D(G) for G to be the square matrix with rows and columns indexed by the vertex set ...

A distance based classification is one of the popular methods for classifying instances using a point-to-point distance based on the nearest neighbour or k-NEAREST NEIGHBOUR (k-NN). The representation of distance measure can be one of the various measures available (e.g. Euclidean distance, Manhattan distance, Mahalanobis distance or other specific distance measures). In this paper, we propose ...

A Euclidean distance matrix is one in which the (i, j) entry specifies the squared distance between particle i and particle j. Given a partially-specified symmetric matrix A with zero diagonal, the Euclidean distance matrix completion problem (EDMCP) is to determine the unspecified entries to make A a Euclidean distance matrix. We survey three different approaches to solving the EDMCP.We advoca...

In machine learning, observation features are measured in a metric space to obtain their distance function for optimization. Given similar that statistically sufficient as population, statistical between two probability distributions can be calculated more precise learning. Provided the observed multi-valued, is still efficient. However, due its scalar output, it cannot applied represent detail...