On the Levy-Desplanques theorem proof: http://planetmath.org/levydesplanquestheorem, they only prove the second inequality for M = i. What about if i ≠ M? e.g. if we are doing it for the first line on a singular matriz and M ≠ 1 we can't get to the second inequality.
I thought that to prove: A strictly diagonally dominant matrix is non-singular (1)
You had to prove: A singular matrix is not strictly diagonally dominant (2).
Howver, they only prove (2) for i = M, whereas it should be for all i!
What am I missing here? I can't understand how proving for only i 0 M constitutes a proof, and I can't prove it for all i.
I thought that to prove: A strictly diagonally dominant matrix is non-singular (1)
You had to prove: A singular matrix is not strictly diagonally dominant (2).
Howver, they only prove (2) for i = M, whereas it should be for all i!
What am I missing here? I can't understand how proving for only i 0 M constitutes a proof, and I can't prove it for all i.
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