Almost Commuting Matrices Need not be Nearly Commuting
Almost Commuting Matrices Need not be Nearly Commuting
Let Mn be the collection of n x n complex matrices with the Hilbert-space-operator norm.There exist two concrete matrices A,B & Mn with \\A\\ = 1 -1/n, ||B|| < 1, \\AB -BA\\ < 2/n, but \\A -R\\ + \\B -S|| > 1 -1/n for all commuting pairs R, S 6 …