Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-04-144-4
DOI: https://dx.doi.org/10.15863/TAS.2025.04.144.4
Language: Russian
Citation: Zhanatauov, S.U. (2025). Transformations of pseudo-eigenvalues in artificial intelligence problems. ISJ Theoretical & Applied Science, 04 (144), 15-23. Soi: https://s-o-i.org/1.1/TAS-04-144-4 Doi: https://dx.doi.org/10.15863/TAS.2025.04.144.4 |
Pages: 15-23
Published: 30.04.2025
Abstract: The numerical matrices Ym5, Z m5 of y- and z–deviations for a system of 5 multi-sense equations are modeled using a mathematical model where the matrices Um5 and Ym5 are separately modeled such that (1/m)UTm5Um5=I55, Y m5 m5=U m5?1/255, Zm5=Um5C55, C55 is the matrix of eigenvectors, ?55 is the matrix of eigenvalues. The matrix ?5555 is transformed from an mm matrix of pseudo-singular numbers of the form ?55=diag(5,(-0.0139), (-0.0077),(0.0105),(0.0111) [1], used in many transformations of several IM PC objects [7-9]. In the article [2], the Optimization Problem is solved, its schematic notation has the form (I55,I55)=>(C55,?55). Optimization Problem [1] gave a solution with a minus sign for the eigenvalues (-0.0139), (-0.0077), it does not satisfy us. In this paper, we have developed a method for converting a matrix of pseudo-singular numbers into a matrix of eigenvalues ?55=diag(5,0.0002, 0.0003, 0.0003,0.0001). It is this model pair (C55,?55) of matrices that is included [3-5] in the new scheme of the Inverse Model of the Principal Components: ((C55, ?55), Z m5, Y m5), used in artificial intelligence and cognitive modeling algorithms.
Key words: algorithms of artificial intelligence and cognitive modeling, multi-semantic equations with semantic variables, mm matrix of pseudo-singular numbers, mm matrix of pseudo-singular vectors.
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