How to display output as symbols?

Question

I have this piece of code which populates a matrix following different rules depending on row and column number:

MQp := Array[Qp, {Length[a], Length[a]}];
Do[Qp[i, 1] = a[[i]], {i, 1, Length[a]}];
Do[Qp[1, j] = a[[j]]/2, {j, 2, Length[a]}];
Do[If[(i == j), 
   If[((2 j - 1) <= Length[a]), Qp[i, j] = a[[2 i - 1]]/2 + a[[1]], 
    Qp[i, j] = a[[1]]], 
   If[(i != 1 && j != 1), 
    If[(i + j - 1) <= Length[a], 
     Qp[i, j] = a[[i + j - 1]]/2 + a[[Abs[i - j] + 1]]/2, 
     Qp[i, j] = a[[Abs[i - j] + 1]]/2]]], {i, 1, Length[a]}, {j, 1, 
   Length[a]}];
Qp[1, 1] = a[[1]];
MatrixForm[MQp]

Currently "a" is a table of numerical values. I would like to generate a table of symbolic a's, and then be able to substitute the numerical values into the matrix. This way I can easily check that the values in the matrix correctly match what should be generated. I've tried several methods, but so far I get errors or nothing is output at all? Can someone help me out? Thanks in advance.

PS: How do I display code blocks correctly? I did a line and eight spaces but it looks like it didn't work.

Answer 1

You can generate an array of symbolic values using Array

Clear[a];
a = Array[A, 5];

Then your matrix MQp becomes:

You can then check for specific values using a pattern. For example,

MQp /. {A[2] -> 3}

gives the matrix with 3 in place of A[2].

Answer 2

Here's is another way to define your matrix using SparseArray[]. Perhaps it's easier to understand:

a = Array[A, 5];
b = SparseArray[{
   {i_, 1} :> a[[i]],
   {1, j_} :> a[[j]]/2,
   {i_, i_} /; (2 i - 1) <= Length@a :> a[[2 i - 1]]/2 + a[[1]],
   {i_, i_} /; (2 i - 1) >  Length@a :> a[[1]],
   {i_, j_} /; (i + j - 1) <= Length[a] :> a[[i + j - 1]]/2 + a[[Abs[i - j] + 1]]/2,
   {i_, j_} /; (i + j - 1) >  Length[a] :> a[[Abs[i - j] + 1]]/2},
  Length@a {1, 1}]
b // MatrixForm