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Sample problems VSB { Technical University of Ostrava Department of Applied Mathematics Petr Kov a r, Tereza Kov a rov a, 2021 The translation was co- nanced by the European Union and the Ministry of Education, Youth and Sports from the Operational Programme Research, Development and Education, project \Technology for the Future 2.0", reg. no.
erations, leading variables, free variables, echelon form, matrix, augmented matrix, Gauss-Jordan reduction, reduced echelon form. 1.1.1. De nition. We will say that an operation (sometimes called scaling) which multiplies a row of a matrix (or an equation) by a nonzero constant is a row operation of type I. An operation
1 sty 2011 · 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 an EDM.We...
There are two fundamental problems associated with distance geometry [10]: 1) given a matrix, determine whether it is an EDM and 2) given a possibly incomplete set of distances, determine whether there exists a configuration of points in a given embed-ding dimension—the dimension of the smallest affine space com-prising the points—that generates...
a) Prove that a linear map T is 1-1 if and only if T sends linearly independent sets to linearly independent sets. b) Prove that T is onto if and only if T sends spanning sets to spanning sets.
1 sty 2011 · Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics,...
A distance matrix is a table that shows the distance between pairs of objects. For example, in the table below we can see a distance of 16 between A and B, of 47 between A and C, and so on. By definition, an object’s distance from itself, which is shown in the main diagonal of the table, is 0.
