Properties of the determinant of a rectangular matrix

Anna Makarewicz; Piotr Pikuta; Dominik Szałkowski

Annales UMCS, Mathematica (2014)

  • Volume: 68, Issue: 1, page 31-41
  • ISSN: 2083-7402

Abstract

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In this paper we present new identities for the Radić’s determinant of a rectangular matrix. The results include representations of the determinant of a rectangular matrix as a sum of determinants of square matrices and description how the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column

How to cite

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Anna Makarewicz, Piotr Pikuta, and Dominik Szałkowski. "Properties of the determinant of a rectangular matrix." Annales UMCS, Mathematica 68.1 (2014): 31-41. <http://eudml.org/doc/266996>.

@article{AnnaMakarewicz2014,
abstract = {In this paper we present new identities for the Radić’s determinant of a rectangular matrix. The results include representations of the determinant of a rectangular matrix as a sum of determinants of square matrices and description how the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column},
author = {Anna Makarewicz, Piotr Pikuta, Dominik Szałkowski},
journal = {Annales UMCS, Mathematica},
keywords = {Determinant of rectangular matrix; Radić’s determinant; determinant of rectangular matrix},
language = {eng},
number = {1},
pages = {31-41},
title = {Properties of the determinant of a rectangular matrix},
url = {http://eudml.org/doc/266996},
volume = {68},
year = {2014},
}

TY - JOUR
AU - Anna Makarewicz
AU - Piotr Pikuta
AU - Dominik Szałkowski
TI - Properties of the determinant of a rectangular matrix
JO - Annales UMCS, Mathematica
PY - 2014
VL - 68
IS - 1
SP - 31
EP - 41
AB - In this paper we present new identities for the Radić’s determinant of a rectangular matrix. The results include representations of the determinant of a rectangular matrix as a sum of determinants of square matrices and description how the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column
LA - eng
KW - Determinant of rectangular matrix; Radić’s determinant; determinant of rectangular matrix
UR - http://eudml.org/doc/266996
ER -

References

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  1. [1] Amiri, M., Fathy, M., Bayat, M., Generalization of some determinantal identities for non-square matrices based on Radic’s definition, TWMS J. Pure Appl. Math. 1, no. 2 (2010), 163-175. Zbl1248.15006
  2. [2] Radić, M., A definition of determinant of rectangular matrix, Glas. Mat. Ser. III 1(21) (1966), 17-22. Zbl0168.02703
  3. [3] Radić, M., About a determinant of rectangular 2 × n matrix and its geometric interpretation, Beitr¨age Algebra Geom. 46, no. 2 (2005), 321-349. 
  4. [4] Radić, M., Areas of certain polygons in connection with determinants of rectangular matrices, Beitr¨age Algebra Geom. 49, no. 1 (2008), 71-96. 
  5. [5] Radić, M., Certain equalities and inequalities concerning polygons in R2, Beitr¨age Algebra Geom. 50, no. 1 (2009), 235-248. 
  6. [6] Radić, M., Suˇsanj, R., Geometrical meaning of one generalization of the determinant of a square matrix, Glas. Mat. Ser. III 29(49), no. 2 (1994), 217-233. Zbl0828.15005

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