Glasnik Matematicki, Vol. 47, No. 1 (2012), 175-180.

ON DETERMINANTS OF RECTANGULAR MATRICES WHICH HAVE LAPLACE'S EXPANSION ALONG ROWS

Mirko Radić and Rene Sušanj

University of Rijeka, Department of Mathematics, 51000 Rijeka, Omladinska 14, Croatia
e-mail: rsusanj@math.uniri.hr

Abstract.   Let A be any given m × n (m ≤ n) matrix over some field and let detA be the determinant of A calculated by Definition 1 given in [1]. Let det^*A denote determinant of A calculated by any other definition which possess Laplace's expansion along rows. Then there exists constant α such that det^*A = α detA.

2010 Mathematics Subject Classification.   51E12.

Key words and phrases.   Determinant of rectangular matrix, Laplace's expansion along rows.

DOI: 10.3336/gm.47.1.15

References:

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2. M. Radić, About a determinant of rectangular 2 × n matrix and it's geometric interpretation, Beiträge Algebra Geom. 46 (2005), 321-349.
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3. M. Radić, Areas of certain polygons in connection with determinants of rectangular matrices, Beiträge Algebra Geom. 49 (2008), 71-96.
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4. M. Radić and R. Sušanj, An application of the determinant of a rectangular matrix in discovering some properties of the pentagon, Glas. Mat. Ser. III 27(47) (1992), 217-226.
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5. R. Sušanj and M. Radić, Geometrical meaning of one generalization of the determinant of a square matrix, Glas. Mat. Ser. III 29(49) (1994), 217-233.
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