1. The problem statement
The problem is from the textbook Mathematics for Physicist by S.M. Lea. it's problem 2.35
The power radiated per unit solid angle by a charge undergoing simple harmonic motion is
\frac{dP}{dΩ} = K \sin^{2}θ \frac{cos^{2}(ωt)}{(1+β \cosθ \sin(ωt))^{5}}
where...
If A or B is singular you get that AXB can be = 0 even if X is not 0 and so obviously T is not a bijection.
If neither are, I'd say that the only way to get AXB = 0 would be to have X = 0
So if AXB= AYB then AX=AY → X=Y. Is that right? and so T is injective .
if Y is in Mn(K). Suppose...
Homework Statement
here's the problem:
Let A and B be n x n matrix with coefficient in K (any field), let Mn(K) be the set of all n x n matrix with coefficient in K . T is a linear map defined like this
T : Mn(K)---> Mn(K)
T(Y) = AYB
what are the necessary conditions for T to be a...