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In this paper, are presented some possibilities for application of an algebraic method which handles XML hierarchical data structures and makes faster the XML search mechanism. The article briefly presents the concepts of Web Services, Service-Oriented Architecture and other modern software paradigms for organization of the processes over internet. The accelerating techniques for XML navigation through linear algebra tools are also discussed. Web Services use the internet as the communication medium and focus on the internet-based standards, which include the Simple Object Access Protocol for transmitting data, Web Services Description Language for defining services, and other message interactions. The presented paper offers one different point of view concerning the building of an algebraic formalism for navigation over XML hierarchy. This nontraditional approach, based on the linear algebra theory, leads to easier interface for XML search techniques that could eliminate some existing language constructions.