how to calculate power of a matrix

I have just started looking at this, so it may be a very simple task to do.

I have a vector of M elements, each element is a matrix 2x2 where the matrix elements A are complex number (real and imaginary or module and phase )

I need to calculate the power^r of this vector. in other words I need to calculate the power^r, where r is a real number, of the matrix A = [ A11 A12 / A21 A22]^r where Axy = Re +Im or Mod and Ph

I'm a new with Matlab, so any suggestion is welcome.

BR Maurizio

Answer 1

[Wayne King]

Are you just asking for the squared modulus (magnitude) of the complex-valued elements of a matrix?

   X = randn(5,5)+1i*randn(5,5);
   abs(X).^2

or if you want to the third power:

   abs(X).^3

[Maurizio Mastorfini]

the matrix is like this:

S11 S12 S21 S22

S = { S11;S12;S21;S22 }

each Sxy is a complex number: re + jim

I need to calculate the S^r where r can be any real number.

The theory says this: find the digonal matrix D of S, which contains the eigenvalues of that matrix S and decompose S in 2 other matrices, called U and V in order to have S = U*D*V the S^r is then calculated in this way

 S^r = U*(D^r) *V

D only has 2 non 0 coefficients: D11 and D22,then

D^r = { D11^r;0;0;D22^r }

I wander if all this can be done with a single funtion, and if the funtion will support a the matrix of complex numbers.

BR

Answer 2

[Azzi Abdelmalek]

r=0.25
A={rand(2)+j*rand(2);rand(2)+j*rand(2);rand(2)+j*rand(2)}
out=cellfun(@(x) x^r,A,'uni',false)
out{:}

if you A^r element by element use

out=cellfun(@(x) x.^r,A,'uni',false)

[Maurizio Mastorfini]

I'll, give this try.. thanks