# How to format linear equation solve

I need to solve the system of linear equations $$S_i = \sum_ {r = 1}^\lambda x_ {r, i} E_r$$, where $$S_i$$ is a $$\lambda$$ - dimensional vector, $$i$$ runs from 1 to $$n$$, $$r$$ runs from 1 to $$\lambda$$, and $$x$$ is a $$\lambda\times n$$ matrix.

I have no idea how to typeset that in Mathematica when I don' t know the values of $$n$$ and $$\lambda$$. The $$S_i$$ come from datasets of different sizes, and I build the $$E_r$$ from said datasets.

Thank you very much in advance.

Edit - Maybe this will help explain beter: I want to avoid having to type

Solve[S[[i,1]]==x[[1,i]]E[[1,1]] + x[[2,i]]E[[1,2]] + ...
&& S[[i,2]]== ...
&& ...
];


for $$\lambda$$ rows, each one with $$\lambda$$ elements. There must be a way to generalise this and typeset in a much simpler way which will then work for any matrix I feed into the code regardless of its dimensions.

Thanks

• What about: eq= Table[S[[i]] == Sum[x[[r, i]] E[[r]], {r, \[Lambda]}], {i, n}] Oct 13, 2021 at 11:00
• @DanielHuber, and then just solve eq for x?
– LNah
Oct 13, 2021 at 22:40
• Yes, eq gives the equations for x Oct 14, 2021 at 7:27

## 1 Answer

Clear["Global*"]

$Version (* "12.3.1 for Mac OS X x86 (64-bit) (June 19, 2021)" *)  You cannot use E as a variable name since it is used for the exponential constant. Use [DoubleStruckCapitalE] instead. $Assumptions = Element[i | λ | n, Integers] &&
i > 0 && λ > 0 && n > 0 &&
Element[\[DoubleStruckCapitalE] | S, Vectors[λ]] &&
Element[x, Matrices[{λ, n}]];

Format[\[DoubleStruckCapitalE][r_]] :=
Subscript[Style[\[DoubleStruckCapitalE], Italic], r];

Format[S[i_]] := Subscript[S, i];

Format[x[r_, i_]] := Subscript[x, r, i]

(eqn = S[i] ==
Sum[HoldForm[x[r, i]*\[DoubleStruckCapitalE][r]], {r,
1, λ}]) // TraditionalForm


eqn // ReleaseHold
`

• Thanks for pointing out that E cannot be used as a variable name. I just used it here as a placeholder, but I'll keep that in mind in the future. From your answer it is still unclear to me (or maybe I was unclear in my original question) how to solve for x. So far what I've tried either throws out errors or gives me a solution of 'x', which is most unhelpful.
– LNah
Oct 13, 2021 at 22:52