So, on a class of matrix-analysis, we've been told that we do not define the supremum and infinum of operators. The 'problem' was the following: We have two matrices, like $$\begin{bmatrix} 1 & 0 \\ 0 & 3\\ \end{bmatrix} $$ and $$\begin{bmatrix} 2 & 0 \\ 0 & 1\\ \end{bmatrix} $$ In this problem we cannot say one is greater / smaller than the other, though we could set an infinum, eg. the identity matrix. However, as he stated, we do not define it for any operator. My question is - why? How can this be proved / did I misunderstand anything?
2026-04-01 10:29:45.1775039385
Supremum / infimum of operators?
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