Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

$$ || A ||_{C^0 (K)} $$ Here $A$ is $ n \times n $ Hermitian, Positive definite matrix, and $K \in \mathbb R^n$.

share|improve this question
    
Hi 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. –  froggie May 13 '12 at 17:17
    
@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. –  Misaj May 13 '12 at 17:24
    
$K$ means that a truncated cone in $R^n$. –  Misaj May 13 '12 at 17:25
2  
In 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 $A$. –  froggie May 13 '12 at 17:26
    
@froggie Oh thank you. There is not any explanation in the book, but I think you're right. –  Misaj May 13 '12 at 17:37
add comment

1 Answer

As the notations may suggest, $K$ is compact and $A(x)$ is a matrix when $x\in K$ and the entries are continuous functions. Then $$\lVert A\rVert_{C^0(K)}=\max_{r,c}\sup\{A_{r,c}(x),x\in K\}.$$

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.