# Can symbolic vectors (not vectors of symbols) be defined and manipulated in the Symbolic Math Toolbox?

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Catalytic on 25 Jun 2019
Commented: Walter Roberson on 9 Feb 2022
I would like to define symbolic functions that are functions of vector-valued quantities, like
syms A x
f(x)=x.'*A*x
where A and x are understood to be a matrix and compatibly-sized vector. I would like to be able to do matrix-vector calculus which gives the result in matrix vector form, such as
G = 2*A*x %I would like this to be the result
I would also like to define functions involving indexing expressions, like
h(x) = x(1) + x(2) + x(3)
Are these things possible? The closest thing I can find is the syntax
x = syms('x',N,1)
but this doesn't seem to behave as I've described. For one thing, manipulations with x do not get simplified to matrix-vector forms.

Walter Roberson on 25 Jun 2019
No this is not possible. Any variable name is expanded to its contents and any symbolic variable names left are assumed to refer to scalar values and expressions will be rewritten assuming scalar communitivity.
Walter Roberson on 9 Feb 2022
Note that a new facility was added as of R2021a; https://www.mathworks.com/help/symbolic/symmatrix.html
I have not had reason to experiment with it yet.

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