Cullis-Radić determinant of a rectangular matrix which has a number of identical columns

Anna Makarewicz, Piotr Pikuta


In this paper we present how identical columns affect the Cullis-Radić determinant of an \(m\times n\) matrix, where \(m\leq n\).


Determinant; rectangular matrix; Cullis-Radić determinant; repeated columns

Full Text:



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.

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

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

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

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

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.

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.

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

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

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).

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

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

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

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

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.

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.

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.

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

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

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.

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.

Data publikacji: 2020-12-28 17:42:00
Data złożenia artykułu: 2020-12-27 17:06:05


Total abstract view - 289
Downloads (from 2020-06-17) - PDF - 161



  • There are currently no refbacks.

Copyright (c) 2020 Anna Makarewicz, Piotr Pikuta