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    Radiation from a moving charge

    Thanks a lot i got it !
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    Radiation from a moving charge

    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...
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    Finding the conditions for a particular mapping to be a bijection

    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...
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    Finding the conditions for a particular mapping to be a bijection

    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...
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