Selection at one locus with multiple alleles

When we discussed selection at one locus with two alleles, I used the following set of viabilities:

$A_1A_1$	$A_1A_2$	$A_2A_2$
$w_{11}$	$w_{12}$	$w_{22}$

You can probably guess where this is going. Namely, I'm going to use $w_{ij}$ to denote the viability of genotype $A_iA_j$. What you probably wouldn't thought of doing is writing it as a matrix

$$\begin{array}{ccc} & A_1 & A_2 \\ A_1 & w_{11} & w_{12} \\ A_2 & w_{12} & w_{22} \end{array}$$

Clearly we can extend an array like this to as many rows and columns as we have alleles so that we can summarize any pattern of viability selection with such a matrix. Notice that I didn't write both $w_{12}$ and $w_{21}$, because (normally) an individual's fitness doesn't depend on whether it inherited a particular allele from its mom or its dad.¹