The radius in matrix algebras--Examples and remarks
Goldberg, Moshe
Original · EN
The main purpose of this note is to illustrate how the radius in a finite-dimensional power-associative algebra over a field F, either R or C, may change when the multiplication in this algebra is modified. Our point of departure will be Fⁿ × ⁿ, the familiar algebra of n × n matrices over F with the usual matrix operations, where it is known that the radius is the classical spectral radius. We shall alter the multiplication in Fⁿ × ⁿ in three different ways and compute, in each case, the radius in the resulting algebra.
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