An in-depth description of an apparently forgotten matrix operation, the reversal operator, is developed. The properties of such an operation are also given, resulting in a new vector-matrix operation resembling the well-known ones of conjugation, transposition, and inversion. The reversal operator operates by ordering the object components where applied. Reversal is easy to perform as it is distributive regarding the vector sum and matrix product. Supplementary descriptions of matrix regions not often used in linear algebra, like the anti-diagonal concept, are also discussed. Some practical problems are given.
References
[1]
Ayres, F. (1970) Matrices (Spanish Version). McGraw Hill.
[2]
Carbó, R. and Domingo, L.L. (1987) Algebra Matricial y Lineal. Schaum-McGraw Hill.
[3]
Wilkinson, J.H. (1965) The Algebraic Eigenvalue Problem. Oxford University Press.
[4]
Wilkinson, J.H. and Reinsch, C. (1971) Handbook for Automatic Computation (II) Linear Algebra. Springer Verlag.
[5]
Durand, E. (1960) Solutions Numériques des Équations Algébriques. Masson.
[6]
Hogben, L. (2007) Handbook of Linear Algebra. Chapman & Hall/CRC.
[7]
Time Reversibility. https://en.wikipedia.org/wiki/Time_reversibility
Chang, J. and Carbó-Dorca, R. (2020) Fuzzy Hypercubes and Their Time-Like Evolution. JournalofMathematicalChemistry, 58, 1337-1344. https://doi.org/10.1007/s10910-020-01137-y
[10]
Gowers, T. (2008) The Princeton Companion to Mathematics. Princeton University Press.
[11]
Carbó-Dorca, R. (2016) Natural Vector Spaces (Inward Power and Minkowski Norm of a Natural Vector, Natural Boolean Hypercubes) and a Fermat’s Last Theorem Conjecture. JournalofMathematicalChemistry, 55, 914-940. https://doi.org/10.1007/s10910-016-0708-6
[12]
Carbó-Dorca, R. (2016) N-Dimensional Boolean Hypercubes and the Goldbach Conjecture. JournalofMathematicalChemistry, 54, 1213-1220. https://doi.org/10.1007/s10910-016-0628-5
[13]
Carbó-Dorca, R. (2016) A Study on Goldbach Conjecture. Journal of MathematicalChemistry, 54, 1798-1809. https://doi.org/10.1007/s10910-016-0649-0
[14]
Carbó-Dorca, R. (2024) Whole Perfect Vectors and Fermat’s Last Theorem. Journal of AppliedMathematicsandPhysics, 12, 34-42. https://doi.org/10.4236/jamp.2024.121004
Carbó-Dorca, R. (2024) Natural Numbers and the Strong Goldbach Conjecture. JournalofAppliedMathematicsandPhysics, 12, 3208-3236. https://doi.org/10.4236/jamp.2024.129192
