How to express a vector which is retrieved from a matrix. In other words, suppose I have a matrix $\mathbf{B},$ y is a the first column vector of the matrix. I am looking for the notation which is involved the matrix.
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$Be_1$ is the first column of $B$, where $e_1$ is the first vector of the standard base. – Itay4 Jul 11 '17 at 13:48
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What is wrong with using a few extra words to make it perfectly clear what it is you are trying to say? I think its better to use words rather than uncommon notation that may instead confuse your reader. Just say what you said here... $y$ is the first column vector of the matrix $B$. No fancy notation needed. – JMoravitz Jul 11 '17 at 14:29
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As Itay4 said on the comments, you can use the standard basis vectors.
$e_1 = \{1,0,0,...,0\}^T$
$e_2 = \{0,1,0,...,0\}^T$
and so on...
The $i_{th}$ row of $B$ is: $r_i = e_i^T\,B$
The $i_{th}$ column of $B$ is: $c_i = B\,e_i$
A general term $(i,j)$ is: $B_{ij} = e_i^T\,B\,e_j$
Daniel Cunha
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