# Homework Help: Need help on understanding this notation

1. Feb 21, 2010

### Firepanda

Where it says maxQ I don't understand.

Q is a matrix, so are A and P.

I know what q1 and the 2-norm of P are, but what on earth does max Q mean?

I started with the matrix A, I've selected Q as positive definite arbitrarily, and I recieved a matrix P. I need to now find rho but I'm stuck on what max Q means.

2. Feb 21, 2010

### n!kofeyn

maxQ means to take the maximum over all possible Q that satisfy the given equation. q1 and P will vary depending on what the matrix Q is.

3. Feb 22, 2010

### Firepanda

I still really don't understand this part, can you simplify it a bit?

Say if I have a matrix Q = [1 2; 3 4]

What is the max Q?

4. Feb 22, 2010

### HallsofIvy

There is no such thing. Matrices are not "ordered" and so do not have "max" or "min".

It's not "max Q", it is $$\begin{array} amax \\ Q\end{array}$$, the maximum taken by a numerical expression over all possible values of Q. This isn't saying anything about a maximum of Q, it's talking about the maximum value of the numerical expression $q_1/||P||$ where Q can be any matrix and P must be such that $A^TP+ PA+ Q= 0$

5. Feb 22, 2010

### Firepanda

Ok thanks, so I don't need to alter the calculation of $q_1/(2||P||)$ and treat it the same as if $$\begin{array} amax \\ Q\end{array}$$ wasn't there?