A generalization of weighted versions of the determinant, permanent and the generalized inverse of rectangular matrices

Subject Areas : Linear and multilinear algebra; matrix theory

M. Bayat ¹

1 - Department of Mathematics, Zanjan Branch, Islamic Azad University, P.O. Box 100190, Zanjan, Iran

Received: 2022-07-03 Accepted : 2022-09-26 Published : 2022-09-28

Keywords:

References:

[1] P. S. Abhimanyu, Defining the determinant-like function for m by n matrices using the exterior algebra, Adv. Appl. Clifford Algebras. 23 (2013), 787-792.

[2] E. Arghiriade, A. Dragomir, Une nouvelle definition de l’inverse generalisée d’une matrice, Rendiconti Lincei. Scienze Fisiche e Naturali. Serie XXXV. 35 (1963), 158-165.

[3] M. Bayat, A bijective proof of generalized Cauchy-Binet, Laplace, Sylvester and Dodgson formulas, Linear. Multilinear. Algebra., In press.

[4] A. Ben-Israel, Generalized inverses of matrices: a perspective of the work of Penrose, Math. Proc. Camb. Phil. Soc. 100 (1986), 407-425.

[5] C. E. Cullis, Matrices and Determinoids, Cambridge University Press, Vol 3, 1925.

[6] R. Gabril, Extinderea Complementilor Algebrici Generalizati la Matrici Oarecare, Studii si Cercetari Matematice. 17-Nr. 10 (1965), 1566-1581.

[7] V. N. Joshi, A Determinant for Rectangular Matrices, Bull. Austral. Math. Soc. 21 (1980), 137-146.

[8] H. Minc, Permanents, Encyclopedia of Mathematics and its Applications, 6, Addison-Wesley, Reading, Mass, 1978.

[9] Y. Nakagami, H. Yanai, On Cullis determinant for rectangular matrices, Linear. Algebra. Appl. 422 (2007), 422-441.

[10] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos Soc. 51 (1955), 406-413.

[11] M. Radic, A definition of determinant of rectangular matrix, Glasnik Matematicki. Ser III. 1 (21) (1966), 17-22.

[12] M. Radic, Areas of certain polygons in connection with determinants of rectangular matrices, Beiträge Algebra Geom. 49 (1) (2008), 71-96.

[13] M. Radic, Inverzije pravokutnih matrica, Doktorska disertacije, 1964.

[14] M. Radic, Some contribution to the inversion of rectangular matricrs, Glasnik Matematicki. Ser III. 1 (21) (1966), 23-37.

[15] M. Radic, R. Susanj, Geometrical meaning of one generalization of the determinant of a square matrix, Glasnik Matematicki. Ser III. 29 (49) (1994), 217-233.

[16] P. Stanimirovic, M. Stankovic, Determinants of rectangular matrices and the Moore-Penrose inverse, Novi Sad J. Math, Vol. 27 (1) (1997), 53-69.

[17] M. Stojakovic, Determinante Nekvadratnih Matrica, Vesnik DMNRS. 1-2 (1952), 9-12.

[18] L. Tan, Signs in the Laplace expansions and the parity of the distinguished representatives, Discrete Math. 131 (1994), 287-299.