Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-06T03:40:02.158Z Has data issue: false hasContentIssue false
  • English
  • Français

Determinants of block matrices

Published online by Cambridge University Press:  01 August 2016

John R. Silvester
John R. Silvester*
Affiliation:
Department of Mathematics, King's College, London WC2R 2LS email: jrs@kcl.ac.uk
Get access Rights & Permissions [Opens in a new window]

Extract

Let us first consider the 2 x 2 matrices and Their sum and product are given by

Here the entries a, b, c, d, e, f, g, h can come from a field, such as the real numbers, or more generally from a ring, commutative or not.

Type
Articles
Information
The Mathematical Gazette , Volume 84 , Issue 501 , November 2000 , pp. 460 - 467
Copyright
Copyright © The Mathematical Association 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Ayres, Frank Jr, Matrices, Shaum’s Outline Series, McGraw-Hill (1962).Google Scholar
2. Mirsky, L. An introduction to linear algebra, Clarendon Press (1955).Google Scholar
3. Artin, E. Geometric Algebra, Interscience (1957).Google Scholar
4. Cohn, P. M. Algebra, Volume 1, 2nd edition Wiley (1982).Google Scholar
5. Zehfuss, G. Über eine gewisse Determinante, Zeitschrift f. Math, u. Phys. 3 (1858) pp. 298–301.Google Scholar
6. Muir, T. The theory of determinants in the historical order of development, Dover reprint (1960).Google Scholar
7. Muir, T. A treatise on the theory of determinants, Macmillan (1882).Google Scholar
8. MacDuffee, C. C. The theory of matrices, Chelsea (1956).Google Scholar
9. Hensel, K. Über die Darstellung der Determinante eines Systems welches aus zwei anderen componirt ist, Acta Math. 14 (1889) pp. 317–319.CrossRefGoogle Scholar
10. Netto, E. Zwei Determinantensätze, Acta Math. 17 (1893) pp. 199–204.CrossRefGoogle Scholar
11. von Sterneck, R. D. Beweis eines Satzes über Determinanten, Monatshefte f. Math. u. Phys. 6 (1895) pp. 205–207.CrossRefGoogle Scholar