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Let $\mathbb{A}_p=\frac{\mathbb{Y}\mathbb{Y}^*}{m}$ and$\mathbb{B}_p=\frac{\mathbb{X}\mathbb{X}^*}{n}$ be two independent randommatrices where $\mathbb{X}=(X_{ij})_{p \times n}$ and $\mathbb{Y}=(Y_{ij})_{p\times m}$ respectively consist of real (or complex) independent randomvariables with $\mathbb{E}X_{ij}=\mathbb{E}Y_{ij}=0$,$\mathbb{E}|X_{ij}|^2=\mathbb{E}|Y_{ij}|^2=1$. Denote by $\lambda_{1}$ thelargest root of the determinantal equation $\det(\lambda\mathbb{A}_p-\mathbb{B}_p)=0$. We establish the Tracy-Widom type universalityfor $\lambda_{1}$ under some moment conditions on $X_{ij}$ and $Y_{ij}$ when$p/m$ and $p/n$ approach positive constants as $p\rightarrow\infty$.

The Tracy-Widom law for the Largest Eigenvalue of F Type Matrix