How to construct a cell array containing a power series of a matrix

Question

Bill Tubbs 2021-5-28

编辑： Bill Tubbs 2021-5-28

I want to compute the following power series of a square matrix A (as a preliminary step to constructing a larger matrix using these results):

results = {A, A^2, A^3, ... , A^n}

where n is variable.

Ideally, I want the result to be a cell array so I can reference them later using an integer index, but a block matrix would also be usable.

Obviously, if A were a scalar this would be quite easy:

>> A = 0.8;
>> results = mat2cell(A.^(1:n),1,ones(1,n))
results =
  1×4 cell array
    {[0.8000]}    {[0.6400]}    {[0.5120]}    {[0.4096]}

It can be done with a for loop:

results = cell(1,n);
X = A;
for i=1:n
    results(i) = {X};
    X = X*A;
end

and I will add another solution below, but I suspect there is a simpler and/or more efficient way.

Answer 1

Bill Tubbs 2021-5-28

编辑：Bill Tubbs 2021-5-28

Here is a solution using cellfun:

results = cellfun(@(i) A^i, num2cell(1:n), 'UniformOutput', false)