An $n \times n$ complex matrix $A$ is called $t$-normal if $A A^{t}=A^{t} A$ where $A^{t}$ is the transpose of $A$. For each $n$, determine the maximum dimension of a linear space of complex $n \times n$ matrices consisting of t-normal matrices. Please provide the value of the dimension when $n = 10$. The answer should be in the format \frac{m}{n}, directly give the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
user