Partially Ordered Group of the 2×2 Symmetric Matrices
DOI:
https://doi.org/10.15408/inprime.v1i2.13701Abstract
AbstractThis paper deals with the partially ordered group of the 2×2 symmetric matrices. A matrix is defined to be a positive if each entry of the matrix is positive. With the characterization of the 2×2 symmetric matrix, we construct the positive cone such that the set of the matrices constructs partially ordered group.
Keywords: Symmetric Matrix, Group-Ordered, Positive Cone.
Abstrak
Artikel ini membahas grup terurut parsial pada matriks simetri berukuran 2×2. Suatu matriks dikatakan positif jika setiap entri pada matriks bernilai positif. Melalui karakteristik dari matriks simetri, akan dikonstruksi sebuah positif cone sehingga matriks simetri berukuran 2×2 merupakan grup terurut parsial.
Kata kunci: Matriks Simetri, Grup Terurut, Positif Cone.
References
I. Herstein, Topics in Algebra., New York: John Willey & Sons, Inc., 1975.
B. MacCluer, Elementary Functional Analysis, New York: Springer, 2009.
J. Ma , Lecture Notes On Algebraic Structure Of Lattice-Ordered Rings, World Scientific,, 2014.
A. Howard and C. Rorres, Elementary Linear Algebra, Ninth Edition, New York: John Willey & Sons, Inc., 2005.
J. Ma and W. Bradley, "Lattice-ordered 2×2 triangular matrix algebras," Linear Algebra Appl., vol. 404, pp. 262-274, 2005.
R. Bhatia, Matrix Analysis, New York: Springer, 1997.
R. Horn and C. Johnson, Matrix Analysis, New York: Cambridge University Press, 1990.
