Use of geometric algebra: Compound matrices and the determinant of the sum of two matrices

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 459, Issue 2030, 2003, Pages 273-285

  Prells, Uwe ^a   Friswell, Michael I ^a   Garvey, Seamus D ^b  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Compound matrices; Determinants; Geometric algebra

Indexed keywords

ARTICLE; CALCULATION; GEOMETRY; MATHEMATICS;

EID: 1542725956     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2002.1040     Document Type: Article

References (23)

1. Aitken, A. C. 1954 Determinants and matrices, 8th edn. Edinburgh: Oliver & Boyd.
2. Amitsur, S. A. 1980 On the characteristic polynomial of a sum of matrices. Linear Multilinear Algebra 8, 177-182.
3. Barret, W. W. & Jarvis, T. J. 1992 Spectral properties of a matrix of Redheffer. Linear Algebra Applic. 162-164, 673-683.
4. Bebiano, N. 1994 New developments on the Marcus-Oliveira conjecture. Linear Algebra Applic. 197-198, 793-803.
5. Bebiano, N., Li, C.-K. & Da Providencia, J. 1994 Determinant of the sum of a symmetric and a skew-symmetric matrix. SIAM J. Matrix Analysis Appl. 18, 74-82.
6. Cullis, C. E. 1913 Matrices and determinoids, vol. 1. Cambridge University Press.
7. Cullis, C. E. 1918 Matrices and determinoids, vol. 2. Cambridge University Press.
8. Cullis, C. E. 1925 Matrices and determinoids, vol. 3, part I. Cambridge University Press.
9. Fuchs, M. B. 1992 The explicit inverse of the stiffness matrix. Int. J. Solids Struct. 29, 2101-2113.
10. Gantmacher, F. R. 1959 The theory of matrices, vols 1 and 2. New York: Chelsea.
11. Horn, R. A. & Johnson, Ch. R. 1985 Matrix analysis. Cambridge University Press.
12. Krattenthaler, C. & Zeilberger, D. 1970 Proof of a determinant evaluation conjectured by Bombieri, Hunt and van der Poorten. New York J. Math. 3, 54-102.
13. Lancaster, P. & Tismenetsky, M. 1985 Theory of matrices, 2nd edn. Academic.
14. Li, C.-K. & Mathias, R. 1995 The determinant of the sum of two matrices. Bull. Austral. Math. Soc. 52, 425-429.
15. Linsay, K. A. & Rooney, C. E. 1992 A note on compound matrices. J. Computat. Phys. 103, 472-477.
16. Malik, R. N. 1970 Compound matrices to the tree-generating problem. IEEE Trans. Circuit Theory 17, 149-151.
17. Marcus, M. 1973 Finite dimensional multilinear algebra, part I. New York: Marcel Dekker.
18. Marcus, M. 1975 Finite dimensional multilinear algebra, part II. New York: Marcel Dekker.
19. Mitrouli, M. & Koukouvinos, C. 1997 On the computation of the Smith normal form of compound matrices. Numer. Algorithms 16, 95-105.
20. Nambiar, K. K. 1997 Hall's theorem and compound matrices. Math. Comput. Modelling 25, 23-24.
21. Nambiar, K. K. & Keating, J. D. 1970 Application of compound matrices to linear systems. IEEE Trans. Circuit Theory 17, 626-628.
22. Porteous, I. R. 1995 Clifford algebras and the classical groups. In Cambridge Studies in Advanced Mathematics. Cambridge University Press.
23. Reutenauer, Ch. & Schützenberger, M.-P. 1987 A formula for the determinant of a sum of matrices. Lett. Math. Phys. 13, 299-302.