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Can anyone show me how to set all matrix rows to variables. For example, I have matrix w={{1,2,3},{3,2,1},{0,0,0}} and I need to set each matrix row to be separate variable that contains the row number of matrix w in its name.

For example, t1={1,2,3} t2={3,2,1} t3={{0,0,0}. Simply it could be done by writing t1=w[[1]] ..., but i have 40 matrices with 200 rows so i need someone to help me do this more efficiently. Variables represents weights in constrained optimization. Thanks in advance.

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    $\begingroup$ I have been using Mathematica for a long time, and in my experience what you are asking for indicates a need to re-think your programming strategy. In every situation I can think of, the rows of a matrix of any size can be accessed without assigning each row to a named variable. $\endgroup$
    – m_goldberg
    Commented Oct 2, 2014 at 9:11
  • $\begingroup$ Thanks for comment. I need these rows as variables because i will use them as a vectors in separate optimization problems,and 3 other expressions which analytics should be provide. $\endgroup$
    – Branimir
    Commented Oct 2, 2014 at 9:29

2 Answers 2

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Perhaps this will work for you. Given a symbol, say t, and a matrix, say m, it will define a set of indexed variables t[1], t[2], ..., t[n], bound to the respective rows of m. 

SetAttributes[assign, HoldFirst];
assign[name_Symbol, matrix_List] := (
  Clear @ name; 
  Do[t[i] = matrix[[i]], {i, 1, Length@matrix}]
  )

Generate some data.

SeedRandom[42];
m = RandomInteger[99, {5, 4}];

{
  {54, 66, 4, 15}, 
  {6, 3, 95, 32}, 
  {48, 3, 81, 87}, 
  {22, 88, 98, 48}, 
  {44, 36, 71, 46}
}

Test

assign[t, m]
DownValues[t]

{
  HoldPattern[t[1]] :> {54, 66, 4, 15}, 
  HoldPattern[t[2]] :> {6, 3, 95, 32}, 
  HoldPattern[t[3]] :> {48, 3, 81, 87}, 
  HoldPattern[t[4]] :> {22, 88, 98, 48}, 
  HoldPattern[t[5]] :> {44, 36, 71, 46}
}
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The code as below can achieve the result that you need.

Clear@t;
mat = RandomInteger[{1, 10}, {20, 4}];
Evaluate[t /@ Range[Length@mat]] = mat

Because of (=)Set has the attribute HoldFirst, I use the function Evaluate to evaluate first before proceeding with Set.

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