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Homework Help
Calculus and Beyond Homework Help
Proof regarding the image and kernel of a normal operator
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[QUOTE="Adgorn, post: 5792749, member: 598632"] [h2]Homework Statement [/h2] Show that if T is normal, then T and T* have the same kernel and the same image. [h2]Homework Equations[/h2] N/A [h2]The Attempt at a Solution[/h2] At first I tried proving that Ker T ⊆ Ker T* and Ker T* ⊆ Ker, thus proving Ker T = Ker T* and doing the same thing with I am T, but could not find a way of doing so. I am relatively certain this has to do with discomposing T into direct sum subspace or doing something with the orthonormal basis of V comprised of eigenvalues of T but I cannot seem to figure it out. I would love some assistance on the matter. [/QUOTE]
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Calculus and Beyond Homework Help
Proof regarding the image and kernel of a normal operator
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