Let $F$ be a vectorial Boolean function from $\mathbb{F}^n$ to $\mathbb{F}^m$, where $m \geq n$. We define $F$ as an embedding if $F$ is injective. In this paper, we examine the component functions of $F$, focusing on constant and balanced components. Our findings reveal that at most $2^m - 2^{m-n}$ components of $F$ can be balanced, and this maximum is achieved precisely when $F$ is an embedding, with the remaining $2^{m-n}$ components being constants. Additionally, for quadratic embeddings, we demonstrate that there are always at least $2^n - 1$ balanced components when $n$ is even, and $2^{m-1} + 2^{n-1} - 1$ balanced components when $n$ is odd.

翻译：设$F$为从$\mathbb{F}^n$到$\mathbb{F}^m$的向量布尔函数，其中$m \geq n$。若$F$为单射，则我们将其定义为嵌入。本文研究了$F$的分量函数，重点关注常数分量与平衡分量。研究结果表明，$F$至多有$2^m - 2^{m-n}$个分量可以是平衡的，且该最大值恰在$F$为嵌入时达到，此时剩余的$2^{m-n}$个分量为常数。此外，对于二次嵌入，我们证明了当$n$为偶数时始终存在至少$2^n - 1$个平衡分量，当$n$为奇数时则存在至少$2^{m-1} + 2^{n-1} - 1$个平衡分量。