Orthogonality Principle for LS solution

Geometric condition for a Least-Squares Solutions: $e=y-Ax\perp\mathcal{R}(A)$

Geometric condition for a Minimum Norm LS Solution: $x\in\mathcal{N}(A)^\perp$

Notes on interesting mathematical objects

Banach space

• A complete linear vector space

Hilbert space

• A complete inner product space (also a Banach space)
• Well defined concept of orthogonality or angle
• Norm induced by the associated inner product

Closed set

• contains all its limit points
• complement of an open set

Complete set (M)

• every Cauchy sequence of points in M has a limit in M
• there are no points missing (inside or at the boundary)

Personalities in RMT

• Roman Vershynin, UMich
• http://www-personal.umich.edu/~romanv/
• Mark Rudelson, U of Missouri
• http://www.math.missouri.edu/~rudelson/
• Mérouane Debbah, Supelec, France
• http://www.flexible-radio.com/merouane-debbah
• Romain Couillet, Supelec, France
• http://couillet.romain.perso.sfr.fr/