Copy the lower triangle to the upper triangle of a matrix to make symmetric matrix

2.19 Copy the lower triangle to the upper triangle of a matrix to make symmetric matrix

Question posted on the net

please help me with simple to apply function that will construct 
symmetric matrix from given just a half matrix with diagonal. 
Eg: 
 
From: 
1  0  0  0 
2  3  0  0 
4  9  5  0 
2  2  3  4 
 
To give: 
 
1  2  4  2 
2  3  9  2 
4  9  5  3 
2  2  3  4

Many answers were given, below is my answer, and I also show how to do it in Matlab

Mathematica

a = {{1, 0, 0, 0}, 
     {2, 3, 0, 0}, 
     {4, 9, 5, 0}, 
     {2, 2, 3, 4}}; 
 
Transpose[LowerTriangularize[a, -1]] + a

 {{1, 2, 4, 2}, 
  {2, 3, 9, 2}, 
  {4, 9, 5, 3}, 
  {2, 2, 3, 4} 
 }

Matlab

a = 
     1     0     0     0 
     2     3     0     0 
     4     9     5     0 
     2     2     3     4 
 
a+tril(a,-1)'

ans = 
     1     2     4     2 
     2     3     9     2 
     4     9     5     3 
     2     2     3     4

Maple

A:=Matrix([[1,0,0,0],[2,3,0,0],[4,9,5,0],[2,2,3,4]]); 
B:=ArrayTools:-LowerTriangle(A,-1); 
A:=A+B^%T;

     [[1,2,4,2], 
      [2,3,9,2], 
      [4,9,5,3], 
      [2,2,3,4]]

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