$$ || A ||_{C^0 (K)} $$ Here $A$ is $ n \times n $ Hermitian, Positive definite matrix, and $K \in \mathbb R^n$.
What does this norm $|| \cdot ||_{{C^0} (K) }$ mean?
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0Hi Ashuley! Could you give more context here? Is $K$ just a point in $\mathbb{R}^n$, or is a compact subset? Are there functions anywhere? Usually $C^0$ denotes the space of continuous functions on some set. – 2012-05-13
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0@froggie oh i'm sorry. In fact, $A$ is consists of functions in $C_b^1$. $C_b^1$ means that the collection of 1 time diff'ble functions with a bounded derivative. – 2012-05-13
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0$K$ means that a truncated cone in $R^n$. – 2012-05-13
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2In that case, my *guess* is that $$\|A\|_{C^0(K)} = \max_{i,j}\sup_{p\in K}|A_{ij}(p)|.$$ Here $A_{ij}$ is the $(i,j)$th entry of $A$. – 2012-05-13
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0@froggie Oh thank you. There is not any explanation in the book, but I think you're right. – 2012-05-13