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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
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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

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