A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive(respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrix A, the sign pattern class of A, denoted Q(A), is defined as {B: sgn(B) = A}. An n by n sign pattern matrix A requires all distinct eigenvalues if every real matrix whose sign pattern is represented by A has n distinct eigenvalues. In this thesis, a number of sufficient and/or necessary conditions for a sign pattern to reuiqre all distinct eigenvalues are reviewed. In addition, for n=2 and 3, the n by n sign patterns that require all distinct eigenvalues are surveyed. We determine most of the 4 by 4 irreducible sign patterns that require four distinct eigenvalues.

This work focuses on a possibility of using current computer vision alghoritms and methods for automatic similarity matching of so called graffiti tags. Those are such graffiti, that are used as a fast and simple signature of their authors. The process of development and implementation of CBIR system, which is created for this task, is described. For the purposes of finding images similarity, local features are used, most notably self-similarity features.