Consider a vector $x \in\mathbb{R}^n$, where I know its projection in all other dimensions smaller than $n$. Can I find projection of $x$ in $\mathbb{R}^m$ where $m > n$.
Please excuse me if I am not using right terminologies as I am not from mathematical background but I can try my best to elaborate my question if there is some ambiguity.
EDIT
As answered by @woofy, If I embed $m-n$ 0's can I be sure it is the right projection? I mean consider $x' \in \mathbb{R}^l$ where $l < n$, and $x'$ is projection of $x$ in $\mathbb{R}^l$ if I embed $n-l$ 0's to $x'$ I will not always get $x$ right?
Okay I got it that there is no unique projection from $\mathbb{R}^n \to \mathbb{R}^m$ if $m>n$. But can we somehow approximate the projection matrix $A \in \mathbb{R}^{m{\times}n}$?
Consider I have $N$ vectors $x_i \in \mathbb{R}^n$, $\forall i \in N$. And for example if I have list of projections in lower dimensions $l$ where $l<n$, means I have all projections matrices $A \in \mathbb{R}^{l{\times}n}$. Can I still not able to approximate the projection of the a vector $x \in \mathbb{R}^n$ in $\mathbb{R}^m$?
You can embed a vector $x=(x_1,x_2,\ldots,x_n)\in\mathbb{R}^n$ in $\mathbb{R}^m$ where $m>n$.
For example, $(x_1,x_2,\ldots,x_n,\underbrace{0,0,\ldots,0}_{m-n})$ is in $\mathbb{R}^m$.