# Notation for matrix that is partially unknown.

I have a matrix with some elements known and some unknown. I am using the notation $A(X)$ where $X$ are the unknown elements (not sure if relevant but I will be solving for the unknown part $X$ later). For example, $$A(x_{11},x_{22})=\left(\begin{array}{cc} x_{11} & 1 \\ 0 & x_{22} \end{array}\right)$$ then $x_{11}$ and $x_{22}$ are unknown.

Is this good notation? Should I be adding something to the notation to make it clearer? Is there better or standard notation for such matrices?

• If you want to give variable names to the unknown positions there's not a better way than you have. Without naming them, some writers just place asterisks (i.e. *) where the unknown entries are. Jul 21 '15 at 6:55
• @coffeemath Thanks. Do you have a reference to a paper / notes (doesn't need to be authoritative) where this is done just to get an idea of how to set things up? Jul 21 '15 at 7:23
• When $x_i$ are not just unknown, but indeed not important to what you are planning to say, the notation with $*$ is used, for example, $\left(\begin{array}{cc} * & 1 \\ 0 & * \end{array}\right)$. See here.
– A.Γ.
Jul 21 '15 at 8:35

$$A(a_{11},a_{22})=\left(\begin{array}{cc} a_{11} & 1 \\ 0 & a_{22} \end{array}\right)\;,$$
and you don't really need to include $a_{11},a_{22}$ as arguments unless you really want to emphasize the dependence, so
$$A=\left(\begin{array}{cc} a_{11} & 1 \\ 0 & a_{22} \end{array}\right)$$
• Thanks. It's important for me to emphasize certain elements. I will be solving for some of the elements in the matrix... I was trying to use notation that's similar to a function $f({\bf x})$ but trying to emphasize that the arguments are just some elements in a matrix. Jul 21 '15 at 7:42
• @user103828: In that case, depending on the context, using $x_{11},x_{22}$ might even be preferable. Jul 21 '15 at 7:49