Entrance examination HEC ESSEC 25: mathematics 1.
In this article, you'll find suggested answers for the Maths approfondies 1 problem set common to both the HEC and ESSEC 2025 competitive entrance exams.
In the first part, we study the adjoint of a linear application.
In the second part, we minimize the quadratic function \[ \begin{alignat*}{1} J_0(X) &= \frac{1}{2}\left\lVert AX - Y \right\rVert^2 \end{alignat*} \] pour \(X\in \mathcal{M}_{p,1}(\mathbb{R})\).
In this section you'll also find a few Python functions and calculations of the expectation of some random variables (you'd better be comfortable with sums with 2, 3 or 4 indices...).
In the third part, we minimize the non-differentiable function \[ \begin{alignat*}{1} J(X) &= \frac{1}{2}\left\lVert AX - Y \right\rVert^2 + \left\lVert BX \right\rVert \end{alignat*} \] pour \(X\in \mathcal{M}_{p,1}(\mathbb{R})\).
The subject ends with 3 Python functions to write.
Temporary document: I haven't proofread it carefully yet.
Correction of the Maths approfondies 1 problem set on April 14 for the BCE HEC ESSEC 2025 competition:
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