Geodesic
An identity between the determinant and the permanent of Hessenberg-type matrices
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 917-921
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this short note we provide an extension of the notion of Hessenberg matrix and observe an identity between the determinant and the permanent of such matrices. The celebrated identity due to Gibson involving Hessenberg matrices is consequently generalized.
In this short note we provide an extension of the notion of Hessenberg matrix and observe an identity between the determinant and the permanent of such matrices. The celebrated identity due to Gibson involving Hessenberg matrices is consequently generalized.
DOI : 10.1007/s10587-011-0059-1
Classification : 05C50, 15A15
Keywords: determinant; permanent; Hessenberg matrices; graphs; trees 
@article{10_1007_s10587_011_0059_1,
     author = {da Fonseca, Carlos Martins},
     title = {An identity between the determinant and the permanent of {Hessenberg-type} matrices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {917--921},
     year = {2011},
     volume = {61},
     number = {4},
     doi = {10.1007/s10587-011-0059-1},
     mrnumber = {2886247},
     zbl = {1249.15011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0059-1/}
}
TY  - JOUR
AU  - da Fonseca, Carlos Martins
TI  - An identity between the determinant and the permanent of Hessenberg-type matrices
JO  - Czechoslovak Mathematical Journal
PY  - 2011
SP  - 917
EP  - 921
VL  - 61
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0059-1/
DO  - 10.1007/s10587-011-0059-1
LA  - en
ID  - 10_1007_s10587_011_0059_1
ER  - 
%0 Journal Article
%A da Fonseca, Carlos Martins
%T An identity between the determinant and the permanent of Hessenberg-type matrices
%J Czechoslovak Mathematical Journal
%D 2011
%P 917-921
%V 61
%N 4
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0059-1/
%R 10.1007/s10587-011-0059-1
%G en
%F 10_1007_s10587_011_0059_1
da Fonseca, Carlos Martins. An identity between the determinant and the permanent of Hessenberg-type matrices. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 917-921. doi: 10.1007/s10587-011-0059-1

[1] Agrawal, M.: Determinant versus permanent. Proceedings of the international congress of mathematicians, Madrid, Spain, August 22-30, 2006 European Mathematical Society Zürich (2006), 985-997. | MR | Zbl

[2] Brualdi, R. A., Shader, B. L.: On sign-nonsingular matrices and the conversion of the permanent into the determinant. Applied geometry discrete mathematics. DIMACS, Ser. Discret. Math. Theor. Comput. Sci. 4 (1991), 117-134. | DOI | MR

[3] Botta, P.: On the conversion of the determinant into the permanent. Can. Math. Bull. 11 (1968), 31-34. | DOI | MR | Zbl

[4] Elsner, L.: A note on generalized Hessenberg matrices. Linear Algebra Appl. 409 (2005), 147-152. | MR | Zbl

[5] Fiedler, M., Vavřín, Z.: Generalized Hessenberg matrices. Linear Algebra Appl. 380 (2004), 95-105. | DOI | MR

[6] Gibson, P. M.: An identity between permanents and determinants. Am. Math. Mon. 76 (1969), 270-271. | DOI | MR | Zbl

[7] Gibson, P. M.: Conversion of the permanent into the determinant. Proc. Am. Math. Soc. 27 (1971), 471-476. | DOI | MR | Zbl

[8] Hwang, S.-G., Kim, S.-J., Song, S.-Z.: On convertible complex matrices. Linear Algebra Appl. 233 (1996), 167-173. | MR | Zbl

[9] Coelho, M. P., Duffner, M. A.: On the relation between the determinant and the permanent on symmetric matrices. Linear Multilinear Algebra 51 (2002), 127-136. | DOI | MR | Zbl

[10] Kräuter, A. R., Seifter, N.: On convertible $(0,1)$-matrices. Linear Multilinear Algebra 13 (1983), 311-322. | DOI | MR | Zbl

[11] Lim, M. H.: A note on the relation between the determinant and the permanent. Linear Multilinear Algebra 7 (1979), 45-47. | MR | Zbl

[12] Marcus, M., Minc, H.: On the relation between the determinant and the permanent. Ill. J. Math. 5 (1961), 376-381. | DOI | MR | Zbl

[13] McCuaig, W.: Pólya's permanent problem. Electron. J. Comb. 11 (2004), Research paper R79. | MR | Zbl

[14] Pólya, G.: Aufgabe 424. Arch. Math. Phys. Ser. 3 20 (1913), 271.

[15] Reich, S.: Another solution of an old problem of Pólya. Am. Math. Mon. 78 (1971), 649-650. | DOI | MR | Zbl

[16] Szegö, G.: Lösung zu Aufgabe 424. Arch. Math. Phys. Ser. 3 21 (1913), 291-292.

[17] Tarakanov, V. E., Zatorskiĭ, R. A.: A relationship between determinants and permanents. Math. Notes 85 (2009), 267-273. | DOI | MR

Cité par Sources :