eigenvalues of a compact positive definite operator!!!
Let A be a compact positive definite operator on Hilbert space H.
Let ψ1,...ψn be an orthonormal set in H.
How to show that <Aψ1,ψ1>+...+<Aψn,ψn> ≤ λ1(A)+...+λn(A), where
λ1≥λ2≥λ3≥..... be the eigenvalues of A in decreasing order.
Can...
Using the definition given below, I wonder whether we can deduce that for each object A in C',
the identity for A in C' coincides with the identity for A in C.
Let C' and C be two categories which satisfies that
(i)each objects in C' belongs to C
(ii)each hom-set in C' is contained in the...
Let f(x) be a continuous functions on [0,∞) and that ∫ |f(t)|^2dt is convergent for 0≤t<∞.
Let ∫ |f(t)|^2dt for 0≤t<∞ equals F.
Show that lim(σ→∞) ∫(1-x/σ)|f(x)|^2 dx for0≤x≤σ converges to F.
I know that it needs to prove that lim(σ→∞) ∫(x/σ)|f(x)|^2 dx for0≤x≤σ converges to 0. Can anyone...
Consider G(n,m), the set of all n-dimensional subsapce in ℝ^n+m.
We define the principal angles between two subspaces recusively by the usual formula.
When I see "Differential Geometry of Grassmann Manifolds by Wong",
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC335549/pdf/pnas00676-0108.pdf
I...