Finding powers of a square matrix

[sylar]

Today in the lecture we have learned the Putzer Algorithm, which enables us to calculate the higher powers(A^n, n>1 an integer) of a square matrix A. The other well-known methods use the Cayley-Hamilton Theorem, and the Jordan form of a matrix. I wonder whether there are other efficient ways to evaluate A^n.

 

[ice109]

i don't know those algos but obviously you can diagonlize the matrix and exponentiate it like that

 

[HallsofIvy]

YOu can't always diagonalize a matrix. That was what he meant by "the Jordan form", for which diagonalizable matrices are a special case.

 

[ice109]

you can use QR decompisition to get a good approximation