Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-06-08T12:56:04.252Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear Transformations on Matrices: The Invariance of a Class of General Matrix Functions

Published online by Cambridge University Press:  20 November 2018

Hock Ong
Hock Ong*
Affiliation:
Tunkn Abdul Rahman College, Kuala Lumpur, Malaysia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let F be a field, F* be its multiplicative group and Mn(F) be the vector space of all n-square matrices over F. Let Sn be the symmetric group acting on the set {1, 2, … , n}. If G is a subgroup of Sn and λ is a function on G with values in F, then the matrix function associated with G and X, denoted by Gλ, is defined by

and let

ℐ(G, λ) = { T : T is a linear transformation of Mn(F) to itself and Gλ(T(X)) = Gλ(X) for all X}.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 937 - 946
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Botta, E. P., Linear transformations on matrices: the invariance of a class of general matrix functions, Can. J. Math. 19 (1967), 281–290.Google Scholar
2. Botta, E. P. Linear transformations on matrices: the invariance of a class of general matrix functions, II, Can. J. Math. 20 (1968), 739–748.Google Scholar
3. Frobenius, G., Uber die Darstellung der endlichen Gruppen durch linear substitutionen: I, Sitzungsberichte der Preuss. Acad. Wiss. zu Berlin (1897), 994–1015.Google Scholar
4. Marcus, M. and May, F. C., The permanent function, Can. J. Math. H(1962), 177–189.Google Scholar
5. Ong, Hock, Linear transformations on matrices: the invariance of generalized permutation matrices-III, Linear Algebra and its Appl. 15 (1976), 119–151.Google Scholar