Cullis-Radić determinant of a rectangular matrix which has a number of identical columns
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 74 (2020) no. 2.

Voir la notice de l'article provenant de la source Library of Science

In this paper we present how identical columns affect the Cullis-Radić determinant of an m× n matrix, where m≤ n.
Keywords: Determinant, rectangular matrix, Cullis-Radić determinant, repeated columns
@article{AUM_2020_74_2_a3,
     author = {Makarewicz, Anna and Pikuta, Piotr},
     title = {Cullis-Radi\'c determinant of a rectangular matrix which has a number of identical columns},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2020_74_2_a3/}
}
TY  - JOUR
AU  - Makarewicz, Anna
AU  - Pikuta, Piotr
TI  - Cullis-Radić determinant of a rectangular matrix which has a number of identical columns
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2020
VL  - 74
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2020_74_2_a3/
LA  - en
ID  - AUM_2020_74_2_a3
ER  - 
%0 Journal Article
%A Makarewicz, Anna
%A Pikuta, Piotr
%T Cullis-Radić determinant of a rectangular matrix which has a number of identical columns
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2020
%V 74
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2020_74_2_a3/
%G en
%F AUM_2020_74_2_a3
Makarewicz, Anna; Pikuta, Piotr. Cullis-Radić determinant of a rectangular matrix which has a number of identical columns. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 74 (2020) no. 2. http://geodesic.mathdoc.fr/item/AUM_2020_74_2_a3/

[1] Amiri, A., Fathy, M., Bayat, M., Generalization of some determinantal identities for non-square matrices based on Radić’s definition, TWMS J. Pure Appl. Math. 1 (2) (2010), 163–175.

[2] Arunkumar, M., Murthy, S., Ganapathy, G., Determinant for non-square matrices, Int. J. Math. Sci. Eng. Appl. 5 (5) (2011), 389–401.

[3] Buraczewski, A., Generalization of formulae of Fredholm type and determinant theory for rectangular matrices, Panamer. Math. J. 1 (2) (1991), 49–66.

[4] Cullis, C. E., Matrices and Determinoids, Vol. 1, Cambridge University Press, Cambridge, 1913.

[5] Joshi, V. N., A determinant for rectangular matrices, Bull. Austral. Math. Soc. 21 (1) (1980), 137–146.

[6] Makarewicz, A., Pikuta, P., Szałkowski, D., Properties of the determinant of a rectangular matrix, Ann. Univ. Mariae Curie-Skłodowska Sect. A 68 (1) (2014), 31–41.

[7] Makarewicz, A., Mozgawa, W., Pikuta, P., Volumes of polyhedra in terms of determinants of rectangular matrices, Bull. Soc. Sci. Lett. Łódz Ser. Rech. Deform. 66 (2) (2016), 105–117.

[8] Nakagami, Y., Yanai, H., On Cullis’ determinant for rectangular matrices, Linear Algebra Appl. 422 (2–3) (2007), 422–441.

[9] Pyle, H. R., Non-square determinants and multilinear vectors, Math. Mag. 35 (2) (1962), 65–69.

[10] Radić, M., A generalization of the determinant of a square matrix and some of its applications in geometry, Matematika (Zagreb) 20 (2) (1991), 19–36 (Serbo-Croatian).

[11] Radić, M., A definition of determinant of rectangular matrix, Glas. Mat. Ser. III 1(21) (1966), 17–22.

[12] Radić, M., About a determinant of rectangular 2 x n matrix and its geometric interpretation, Beitrage Algebra Geom. 46 (2) (2005), 321–349.

[13] Radić, M., Areas of certain polygons in connection with determinants of rectangular matrices, Beitrage Algebra Geom. 49 (1) (2008), 71–96.

[14] Radić, M., Certain equalities and inequalities concerning polygons in R2, Beitrage Algebra Geom. 50 (1) (2009), 235–248.

[15] Radić, M., Susanj, R., An application of the determinant of a rectangular matrix in discovering some properties of the pentagon, Glas. Mat. Ser. III 27(47) (2) (1992), 217–226.

[16] Radić, M., Susanj, R., On determinants of rectangular matrices which have Laplace’s expansion along rows, Glas. Mat. Ser. III 47(67) (1) (2012), 175–180.

[17] Radić, M., Susanj, R., Trinajstic, N., Certain classes of polygons in R2 and areas of polygons, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 16(503) (2009), 7–12.

[18] Stojakovic, M., Determinant of non-square matrix, Bull. Soc. Math. Phys. Serbie 4 (1952), 9–23 (Serbo-Croatian).

[19] Sudhir, A. P., On the determinant-like function and the vector determinant, Adv. Appl. Clifford Algebr. 24 (3) (2014), 805–807.

[20] Susanj, R., Radic, M., Geometrical meaning of one generalization of the determinant of a square matrix, Glas. Mat. Ser. III 29(49) (2) (1994), 217–233.

[21] Yanai, H., Takane, Y., Ishii, H., Nonnegative determinant of a rectangular matrix: Its definition and applications to multivariate analysis, Linear Algebra Appl. 417 (1) (2006), 259–274.