How can i build a symmetric matrix from a vector ?

assume i have a 1*n vector like x = [1 2 3 4 5 6], i want to reshape this vector to a symmetric matrix like

symx = [1 2 3; 2 4 5; 3 5 6];

or something like this:

symx = [1 4 6; 4 2 5; 6 5 3];

Thanks for your help

[John D'Errico]

Sorry, but unless you give the rules by which you have chosen to call that a "reshape" where you take 6 numbers and somehow magically decide to reshape them into a 9 element array, then nobody can help you. The mind reading toolbox is still in beta test.

Answer 1

[Moe Money]

I used the functions SQUAREFORM and DIAG

Example: Imagine you want to create a symmetric 4x4 matrix. You need a vector with 10 elements.

>> n=4;

>> vec=[1:10]';

>> sqmat = diag(vec(1:n)) + squareform(vec(n+1:end))

sqmat =

     1     5     6     7
     5     2     8     9
     6     8     3    10
     7     9    10     4

Answer 2

[Steven Lord]

The SQUAREFORM function from Statistics and Machine Learning Toolbox gets close, but it puts zeros on the diagonal and fills in the upper and lower triangles, which is not quite what you're asking for but is close. In order to do what you're asking, you can use logical indexing.

 x = 1:6;
 y = zeros(3);
 upperTriangleIndices = triu(true(3));
 y(upperTriangleIndices) = x; % Fill in the upper piece
 y = y + y.' - diag(diag(y)) % Mirror the upper piece to the lower, which doubles the diagonal
                             % so subtract off the diagonal

[sajjad]

Thanks, Steven i think i find the way just when i send my question to the forum, the answer is using the vec2sm function.

[Moe Money]

Steven: I had a similar question and the function SQUAREFORM solved my problem. Thanks a lot!

Answer 3

[Walter Roberson]

http://www.mathworks.com/help/matlab/ref/toeplitz.html