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matlabmatrixvectorsymmetric

Create a Symmetric Matrix from a vector in MATLAB

How to covert vector A to symmetric matrix M in MATLAB

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Such that M is a symmetric matrix (i.e. A21=A12) and all diagonal terms are equal (i.e. A11=A22=A33=A44).

Solution

  • Use hankel to help you create the symmetric matrix, then when you're finished, set the diagonal entries of this intermediate result to be the first element of the vector in A:

    M = hankel(A,A(end:-1:1));
M(eye(numel(A))==1) = A(1);

    Example

    >> A = [1;2;3;4]

A =

     1
     2
     3
     4

>> M = hankel(A,A(end:-1:1));
>> M(eye(numel(A))==1) = A(1)

M =

     1     2     3     4
     2     1     4     3
     3     4     1     2
     4     3     2     1

    As you can see, M(i,j) = M(j,i) except for the diagonal, where each element is equal to A(1).