How to create a symbolic matrix which is symmetric?

Hello, I essentially want to create something with the form you would get from doing:

   A = sym('A', [6,6])

but additionally I would like A to be symmetric and I'm not sure if there is an easy way to generate this?

Answer 1

[John D'Errico]

A = sym('A', [6,6]);

A = tril(A,0) + tril(A,-1).'
A =
[ A1_1, A2_1, A3_1, A4_1, A5_1, A6_1]
[ A2_1, A2_2, A3_2, A4_2, A5_2, A6_2]
[ A3_1, A3_2, A3_3, A4_3, A5_3, A6_3]
[ A4_1, A4_2, A4_3, A4_4, A5_4, A6_4]
[ A5_1, A5_2, A5_3, A5_4, A5_5, A6_5]
[ A6_1, A6_2, A6_3, A6_4, A6_5, A6_6]

Looks symmetric to me.

[Walter Roberson]

Note: some languages permit you to mark symmetry as a property of symbolic matrices, so that if you assign into an element of the matrix then the symmetric location is automatically updated. The Symbolic Engine does not appear to support that feature, and there is no interface to such a feature from the MATLAB level of the Symbolic Toolbox.

[Will Bolton]

Hmm so now I have the issue with this method that if I want to solve with this matrix, when I plug it back in I get the error:

One or more variables are used multiple times. Cannot distinguish between variables and equations. Use a vector of equations and a vector of variables to avoid ambiguity.

I essentially have a system of equations in the lower triangle of a matrix, with the upper portion all zeroes. I am trying to solve in terms of the elements of the symmetric matrix. There are the same number of variables as there are equations but what I'm trying isn't working. I have tried:

sol = solve(eqn, W)
sol = solve(eqn, tril(W))

The former gets the error above, the latter gets:

The second argument must be a vector of symbolic variables.

[Walter Roberson]

sol = solve(eqn, unique(W))