Mar 29, 2023 · But how can i proof that KerT ∩ ImT = {0} K e r T ∩ I m T = {0} or disprove it linear-algebra linear-transformations Cite edited Apr 4, 2023 at 10:16

Dec 21, 2014 · Let X,Y be two normed spaces, and T: X → Y T: X → Y a bounded linear operator. prove that the adjoint operator T∗ T ∗ (T∗f(x) = f(Tx) T ∗ f (x) = f (T x) is injective iff ImT I m T is …

Linear Tranformation that preserves Direct sum V = ImT ⊕ KerT V = I m T ⊕ K e r T Ask Question Asked 12 years, 6 months ago Modified 12 years, 6 months ago

May 26, 2023 · Let V V be a finite dimensional inner product space and T: V → V. T: V → V Prove Ker T =(T = (Im (T∗))⊥ T ∗)) ⊥ and ((Ker T∗)⊥ T ∗) ⊥ = Im T T. Deduce dimIm T T = dimIm T∗ T …

Mar 1, 2015 · Let T: V → W T: V → W be linear transformation and V have a finite dimension. Show that ImTt = (kerT)° I m T t = (k e r T) ° I have to prove it by mutual inclusion. I have …

Dec 13, 2024 · Now, my problem arises when I evaluate P_imT with specific values of a,b,c (in this case, the standard basis of C3 C 3) in order to obtain the columns of the projection matrix …

Let T: V → W T: V → W be a linear transformation, then Ann(ImT) = kerT∗ Ann (Im T) = ker T ∗. How one could start to prove it? Many thanks.

What's the difference between T (V) and ImT? Ask Question Asked 12 years, 4 months ago Modified 12 years, 4 months ago

Jul 19, 2021 · for part d, would elaborate by showing that the image of T T is equal to the span of x x. Since you already know that and x x are linearly independent, then the set x x is a basis of …

Jan 27, 2021 · So I know this can be true for when T:R -> R, but does this apply for when R is raised to any power? Would this also work if, for example, we had R^3? Thanks in advance