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I want to get familiar with computing sup-norms of diagonalizable operators on $\mathbf{R}^n$. Suppose that I have a diagonalizable linear map $T:\mathbf{R}^n\to \mathbf{R}^n$ and I consider $\mathbf{R}^n$ with its standard norm. Then, what is the norm of $T$ in terms of its eigenvalues?

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If $\mathbb R^n$ is equipped with the euclidean norm, then the norm of a orthogonally diagonizable operator $T\colon\mathbb R^n\to\mathbb R^n$ is the supremum of the absolute values of the eigenvalues of $T$. Is this what you were asking for?

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    @Rasmus: Thanks (+1).2011-12-06