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Let us consider the euclidean norm on $\mathbf{R}^2$. After some computations, I have obtained the following expression for the associated operator norm on 2 by 2 matrices. $$ \left\lVert\pmatrix{a&...

Let $X$ be a finite dimensional Banach space and define a matrix norm $\| \cdot \|_{X}$ by $$ \| A \|_{X} = \sup_{x \ne 0} \frac{\|A x\|_{X}}{\|x\|_{X}} $$ where the matrix $A$ is interpreted as an ...