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What is the range of the map $\mathbb{C}^m\to\mathbb{C}^m$,
$$(z_1,\ldots,z_m)\mapsto (b_1,\ldots,b_m),$$
where $b_k=\prod_{j\neq k}(z-z_j)$$b_k=\prod_{j\neq k}(z_j-z_k)$ for $1\leq k\leq m$ ?
What is the range of the map $\mathbb{C}^m\to\mathbb{C}^m$,
$$(z_1,\ldots,z_m)\mapsto (b_1,\ldots,b_m),$$
where $b_k=\prod_{j\neq k}(z-z_j)$ for $1\leq k\leq m$ ?
What is the range of the map $\mathbb{C}^m\to\mathbb{C}^m$,
$$(z_1,\ldots,z_m)\mapsto (b_1,\ldots,b_m),$$
where $b_k=\prod_{j\neq k}(z_j-z_k)$ for $1\leq k\leq m$ ?
LetWhat is the range of the map$z_1, z_2,\cdots, z_m \in \mathbb{C}$ and$\mathbb{C}^m\to\mathbb{C}^m$,
$$(z_1,\ldots,z_m)\mapsto (b_1,\ldots,b_m),$$
where$z_i\neq z_j$$b_k=\prod_{j\neq k}(z-z_j)$ for$i\neq j$. If$a_i=\frac{1}{\prod _{j\neq i}(z_j-z_i)}$, then what about the rang of$[a_1,\cdots, a_m]$ in$1\leq k\leq m$$\mathbb{P}^{m-1}$?
Let$z_1, z_2,\cdots, z_m \in \mathbb{C}$ and$z_i\neq z_j$ for$i\neq j$. If$a_i=\frac{1}{\prod _{j\neq i}(z_j-z_i)}$, then what about the rang of$[a_1,\cdots, a_m]$ in$\mathbb{P}^{m-1}$?
What is the range of the map$\mathbb{C}^m\to\mathbb{C}^m$,
$$(z_1,\ldots,z_m)\mapsto (b_1,\ldots,b_m),$$
where$b_k=\prod_{j\neq k}(z-z_j)$ for $1\leq k\leq m$ ?
