# If every elements of a matrix convergence in probability, do this matrices converge in probability?

Let $$\widehat{\sum}=\left(a_{i,j}^{N}\right)_{1\leq i\leq j\leq N}$$ and $$\sum=\left(a_{i,j}\right)_{1\leq i\leq j\leq N}$$.

If $$a_{i,j}^{N}\overset{P}{\to} a_{i,j}$$ for any $$1\leq i\leq j\leq N$$, then $$\widehat{\sum}\overset{P}{\to} \sum$$? Is this true or are there additional conditions required?