Inner Product Space

Results named in Tau Ceti's TauCeti.Analysis.InnerProductSpace modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

Bessel's inequality for a… to The interval/exterior Sylvester…

• Bessel's inequality for a functional
• Cauchy–Schwarz for the column series
• The Cotlar–Stein lemma
• Courant–Fischer, lower direction
• Davis's eigenvalue-change lower bound
• Davis's sin 2θ theorem, angle form
• The Davis–Kahan sin 2Θ theorem
• The dimension-free Davis–Kahan sin Θ theorem for the gap
• The dimension-free directed Davis–Kahan sin Θ theorem
• The directed Davis–Kahan sin Θ theorem for the directed gap
• Forward Schur–Horn inequality, Karamata form
• Frobenius identity for the overlap operator
• The Frobenius Sylvester bound
• The Frobenius upper residual bound
• Hadamard's inequality
• Hilbert–Schmidt norm identity
• The Hoffman–Wielandt inequality
• Hopf's boundary-point lemma
• Horn's theorem (LinearMap.IsSymmetric.exists_orthonormalBasis_re_inner_apply_self_eq_of_mem_convexHull)
• The interval/exterior Sylvester bound

Ky Fan perturbation sin Θ… to The Schwarz reflection principle

• Ky Fan perturbation sin Θ bound
• Ky Fan residual sin Θ bound
• Ky Fan's maximum principle, attainment
• Ky Fan's trace inequality
• Lions' representation theorem
• Liouville theorem under the sign condition f · Δ f ≥ 0
• The Lipschitz bound for bounded harmonic functions
• The pairwise π / 2 Davis–Kahan sin Θ theorem
• Parseval's identity for a functional
• The pointwise Clarkson inequality
• Population-gap Frobenius sin-theta theorem
• Population-gap sine theorem for arbitrary ordered eigenframes
• Pythagorean Gram identity for complementary linear blocks
• The Rayleigh lower bound
• The Rayleigh principle
• The rectangular double-angle Gram identity
• Reflected cross-block Gram identity for linear blocks
• The reverse separated Sylvester bound
• The Schur–Horn theorem (LinearMap.IsSymmetric.range_re_inner_apply_self_eq_convexHull_eigenvalues_comp_perm)
• The Schwarz reflection principle

The separated Sylvester bound to The Yu–Wang–Samworth overlap…

• The separated Sylvester bound
• The singular-value Hoffman–Wielandt inequality
• The spectral theorem for compact normal operators
• Spectral theorem for normal operators
• The spectral theorem for the solution operator
• Sylvester bound from a disc and the exterior of a larger disc
• The variational Fredholm alternative
• The von Neumann trace inequality
• Von Neumann's criterion
• von Neumann's theorem
• Weyl's additive inequality, upper form
• Weyl's inequality
• Weyl's lemma for continuous functions
• Young's inequality for real inner products
• Yu–Wang–Samworth bound for left singular vectors
• The Yu–Wang–Samworth overlap bound, Frobenius form

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