We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The formula is expressed in terms of a definite integral with parameters. We derive a differential equation satisfied by the integral for the $2 \times 2$ matrix case and perform a numerical analysis of it.

中文翻译：

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计算实数非中心 Wishart 矩阵的最大特征值的预期欧拉特征

我们通过一般维数的期望欧拉特征法给出了实Wishart矩阵的最大特征值分布的近似公式。该公式用带参数的定积分表示。我们推导出满足 $2 \times 2$ 矩阵情况的积分的微分方程，并对其进行数值分析。