All Questions

How can we characterize the set of all injective functions from $\mathbb{R}^d$ to the set of all symmetric positive definite matrices of dimension d?

Let $X \in \mathbb{R}^{n \times d}, w \in \mathbb{R}^d, y \in \{\pm 1 \}^{n}, \alpha \in (0, 1)$. Consider the equation $$ X^{\top}(Xw-y)+\alpha \|w\|_{2}X^{\top}\operatorname{sign}(Xw-y)+\alpha\frac{...

Let $Y \in \mathbb R^{n \times c}$ and $r$ be an integer with $1 \le r \le \operatorname{rank}(Y)$. Consider the problem $$\text{minimize} \|Y-X\|_{\text{Fro}}^2\text{ over }X \in \mathbb R^{n \times ...