# Given a matrix $M$ how to form the following matrix $N$ from $M$.

Given a matrix $M$ how to form the following matrix $N$ from $M$.

Suppose $M=$\begin{bmatrix} 0 &3 \ 2 &0 \end{bmatrix}

Here $M$ is a $2\times 2$ matrix with 1st row $[0,3]$ and 2nd row $[2,0]$.

We need to form $N$ such that

$N=$ \begin{bmatrix} 3& 3\ 2&2\end{bmatrix}

Here $N$ is a $2\times 2$ matrix with 1st row $[3,3]$ and 2nd row $[2,2]$.

Thus $N$ is formed from $M$ by just adding all the off the diagonal elements of $M$ in a given row to the diagonal element

So the diagonal element of $N$ is the sum of all the remaining entries in a given row of $M$ whereas the rest of the elements of $N$ are the same as $M$.

So the elements of $N$ are obtained from $M$ in the following way :

$a_{11}=0+3=3, a_{12}=3,a_{21}=2,a_{22}=2+0=2$

How to code it?

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Given a matrix M, you can get its ith row with M.row(i), and the sum of its values with sum(M.row(i)). Now you just have to make a loop and modify diagonal elements step by step:

def myfunc(M):
assert M.is_square()
d,e = M.dimensions()
N = copy(M)
for i in range(d):
N[i,i] = sum(N.row(i))
return N


We have:

sage: M = matrix(2,2,[0,3,2,0])
sage: M
[0 3]
[2 0]
sage: myfunc(M)
[3 3]
[2 2]

more