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All Journal AL-ULUM: JURNAL SAINS DAN TEKNOLOGI
Mubikayi Kabumvu Serge
University of Kinshasa, Democratic Republic of Congo.
Agriculture, Biological Sciences & Forestry Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Decision Sciences, Operations Research & Management Energy

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ON THE KERNEL METHOD COMPARED TO THE MATRIX INVERSION METHOD FOR PASSING FROM A DUAL BASIS TO THE BASIS OF A VECTOR SPACE Michael Kilela Makiese; Pongo Ngentshi Benoit; Milolo Kanimuambidi Lea-Irene; Bompoma Elese Ruphin; Mubikayi Kabumvu Serge
AL ULUM: JURNAL SAINS DAN TEKNOLOGI Vol 11, No 2 (2025)
Publisher : UPT Publication and Journal Management, Islamic University of Kalimantan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31602/jst.v11i2.19337

Abstract

In this work, we study and compare two methods for passing from a dual basis to the basis of a finite-dimensional vector space by recalling the passage from a basis to its dual. For the inverse transition, we clarify the kernel method for linear forms and the matrix inversion method, the former exploiting the properties of linear forms and orthogonality, while the latter relies on the explicit inversion of transition matrices, with remarks for each approach depending on the context of application. The study shows that, although matrix inversion is a more direct method, the kernel method can offer a more elegant and efficient alternative in certain cases, especially when the vector space has particular structures.
Co-Authors Bompoma Elese Ruphin Michael Kilela Makiese Milolo Kanimuambidi Lea-Irene Pongo Ngentshi Benoit