#### 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:* `mradic@ffri.hr`
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 det*A* 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 det*A*.

**2010 Mathematics Subject Classification.**
51E12.

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

**Full text (PDF)** (free access)
DOI: 10.3336/gm.47.1.15

**References:**

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*A definition of the determinant of a rectangular matrix*, (Serbo-Croatian summary)
Glas. Mat. Ser. III **1(21)** (1966), 17-22.

MathSciNet

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MathSciNet

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*Areas of certain polygons in connection with determinants of rectangular matrices*, Beiträge Algebra Geom. **49** (2008), 71-96.

MathSciNet

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*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.

MathSciNet

- 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.

MathSciNet

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