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Lets say I have a 100 row by 200 column matrix $\phi$, is there any standard notation or something which defines the vector $\Phi$ which has the same amount of columns (i.e. 200 columns), but all the rows summed up into just one row?

Something like we use $\sum$ for elements of a set or iterating over a sequence.

jbx
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2 Answers2

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Simply put, $\Phi=(1,1,\ldots,1)\phi$.

user1551
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  • Thanks. I was wondering whether there was some notation for this, because it seems like something people use often. – jbx Oct 17 '13 at 17:42
  • @jbx I don't think there is a notation for this, at least not a popular one, but in some occasions, people will write "$\Phi=e^\top\phi$", "$\Phi=\mathbf{1}^\top\phi$" or "$\Phi=u^\top\phi$", and states that $e$ or $\mathbf{1}$ or $u$ means "a vector of ones". In other occasions, people may simply refer to $\Phi$ as "the sum of all rows of $\phi$". – user1551 Oct 17 '13 at 17:49
  • Thanks, $1^T\phi$ and separately specifying that $1$ is a vector of (1,1, ..., 1) seems acceptable. – jbx Oct 17 '13 at 17:59
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The Rencher & Schaalje book on linear models uses the notation $\mathbf{j} = (1,1, ..., 1)$, where $\mathbf{j}$ is a column vector of $1$s. Then $ \mathbf{j'A} $ is the column sums of $\mathbf{A}$, and $\mathbf{Aj}$ is the row sums of $\mathbf{A}$.

If you want the column sums of $\phi$, we have $\mathbf{\Phi} = \mathbf{j}'\phi$.

patr1ckm
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