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How to define the following matrix like the following?

Licheng Zhang
Posted 6 years ago

How to define the following matrix: the order of matrix is n, In other word, I want define the matrix function of n and i represents the imaginary unit. enter image description here

POSTED BY: Licheng Zhang
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You can define a function like so:

bandMatrix[dim_Integer] := Module[{mat},
  mat = SparseArray[{Band[{1, 1}] -> 0, Band[{2, 1}] -> I, Band[{1, 2}] -> I}, {dim, dim}];
  mat[[1, dim]] = mat[[dim, 1]] = 1;
  Return[Normal[mat]]
  ]

enter image description here
POSTED BY: Henrik Schachner
J. M.
J. M.
Posted 6 years ago

Band[{1, 1}] -> 0 can be omitted, certainly. Also, you can put in the assignments of the corner elements in SparseArray[] itself. Thus,

With[{n = 5}, 
     SparseArray[{Band[{2, 1}] -> I, Band[{1, 2}] -> I,
                  {1, -1} -> 1, {-1, 1} -> 1}, {n, n}]] // MatrixForm
POSTED BY: J. M.
Licheng Zhang
Licheng Zhang
Posted 6 years ago

Very thanks to you
POSTED BY: Licheng Zhang
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