0
$\begingroup$

I've searched for this but I'm having some trouble following the answers from other threads. It's probably quite simple. I'm looking for an upper bound on the eucledian norm of a square,real, n x n matrix, A. The matrix is time varying, with the variables in this matrix are all bounded. How do I go about this? I am very mathematically rusty.

Best Regards MC

$\endgroup$

2 Answers 2

0
$\begingroup$

We have $A(t)=(a_{ij}(t))$ and there are numbers $c_{ij} \ge 0$ such that

$|a_{ij}(t)| \le c_{ij}$ for all $t$ in the domain of $A$

($i,j =1,...,n$).

Define $C=(c_{ij})$.

It is your turn to show that

$||A(t)|| \le ||C||$ for all $t$ in the domain of $A$ .

$\endgroup$
0
$\begingroup$

\begin{align*} \|A\|_{Fr} &= \sqrt{\sum_{i,j=1}^n|a_{ij}|^2} \leqslant \sqrt{\sum_{i,j=1}^nc_{ij}^2}\leqslant n^2c \end{align*}

With $|a_{ij}|\leqslant c_{ij}$, the bound of each element, and $c:=\max_{ij}c_{ij}$.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .