# Symbolic matrix multiplication to polynomial

**URL:** <https://discourse.julialang.org/t/symbolic-matrix-multiplication-to-polynomial/93679>\
**Category:** General Usage\
**Created:** [January 28, 2023, 8:59am UTC](https://discourse.julialang.org/t/symbolic-matrix-multiplication-to-polynomial/93679 "2023-01-28T08:59:01Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![jar1](https://avatars.discourse-cdn.com/v4/letter/j/c0e974/32.png) [@jar1](https://discourse.julialang.org/u/jar1)\
**Post date:** [January 28, 2023, 8:59am UTC](https://discourse.julialang.org/t/symbolic-matrix-multiplication-to-polynomial/93679/1 "2023-01-28T08:59:01Z")

</div>

Can I get a polynomial out of this?

```julia
julia> @variables x[1:3] y[1:3] 
3-element Vector{Symbolics.Arr{Num}}:
 x[1:3]
 y[1:3]

julia> A = [
            1 2 14
           -5 2 -3
            8 19 -2
       ]
3×3 Matrix{Int64}:
  1 2 14
 -5 2 -3
  8 19 -2

julia> y'A*x
adjoint([1 -5 8; 2 2 19; 14 -3 -2]*y)*x

julia> collect(y'A*x)
0-dimensional Array{Num, 0}:
adjoint([1 -5 8; 2 2 19; 14 -3 -2]*y)*x

```

---

<div class="post-metadata">

**Author:** ![baggepinnen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baggepinnen/32/693_2.png) [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)\
**Post date:** [January 28, 2023, 9:46am UTC](https://discourse.julialang.org/t/symbolic-matrix-multiplication-to-polynomial/93679/2 "2023-01-28T09:46:57Z")

</div>

Collect the array variables immediately

```julia
julia> x,y = collect.((x,y))
(Num[x[1], x[2], x[3]], Num[y[1], y[2], y[3]])

julia> y'A*x
(14y[1] - 3y[2] - 2y[3])*x[3] + (8y[3] + y[1] - 5y[2])*x[1] + (2y[1] + 2y[2] + 19y[3])*x[2]

```