Symbol for excluding one element of a vector Let $x_i \in x := (x_1,\ldots,x_n)$. I want to define $x_{-i}$ such that $x_{-i}$ contains every element of $x$ except $x_i$, i.e. $x_i \not \in x_{-i}:=(\ldots,x_{i-1},x_{i+1},\ldots)$. 


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*Is there some symbol like setminus, say $x_{-i}:= x \setminus x_i$?

 A: I believe it was Richard Rado, author of many notational innovations, who introduced the so-called obliteration sign, a hat placed over an element of a sequence to indicate its deletion:

$$(x_1,\dots,\hat x_i,\dots,x_n)=(x_1,\dots,x_{i-1},x_{i+1},\dots,x_n)$$

A: I do not know of any such notation, but you could define a crippling matrix:
$${\bf C}_{i} = \left[\begin{array}{lll}{\bf I}_{i-1}&0&0\\0 & 0 & {\bf I}_{n-i} \end{array}\right]$$
This matrix is an identity matrix which has had it's $i$th row removed and everything else intact so that if we multiply from the left:
$${\bf C}_i{\bf x}$$
then he first $i-1$ entries will be copied from $\bf x$ by the first identity matrix, then one skipped, and the remaining copied. This way you could use algebra with these matrices instead of having a need for adding notation on to the vectors themselves ( which usually just add a source of confusion anyway ).

Edit 
${\bf C}_i$ assumes $\bf x$ is column, but it will of course work for row vectors ${\bf x}^T$ by doing the transpose:
$${\bf x}^T {{\bf C}_i}^T$$

As an example
$$\left[\begin{array}{cccccc}
1&0&0&0&0&0\\
0&1&0&0&0&0\\
0&0&1&0&0&0\\
0&0&0&0&1&0\\
0&0&0&0&0&1
\end{array}\right] \left[\begin{array}{c}x_1\\x_2\\x_3\\x_4\\x_5\\x_6\end{array}\right] = \left[\begin{array}{c}x_1\\x_2\\x_3\\x_5\\x_6\end{array}\right]$$
