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Powers of a matrix

  1. Jun 12, 2010 #1
    We know how to calculate a integral powers of a matrix but how can we find rational fractional powers and irrational powers??
     
  2. jcsd
  3. Jun 12, 2010 #2

    phyzguy

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    Science Advisor

    The best way is to expand the result in a power series about the identity matrix. Then you can write:
    [tex]M^a = I + a (M-I) + \frac{a(a-1)}{2}(M-I)^2 + ...[/tex]
     
  4. Jun 12, 2010 #3
    I is identity matrix of which order??
    Let M is 4[tex]\times3[/tex] then what will be the order of I???
     
  5. Jun 12, 2010 #4

    Borek

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    Staff: Mentor

    Is it at all possible to calculate any power of a non square matrix? What will be M2 in your case?
     
  6. Jun 12, 2010 #5
    Soory Morek
     
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