How to calculate matrixA^100 manually

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To calculate A^100 of a 3x3 matrix manually, consider using properties of the matrix such as diagonalizability or Jordan form, which can simplify the computation. If the matrix is diagonalizable, expressing it in terms of its eigenvalues can facilitate the calculation. Alternatively, the minimal polynomial can be employed to express A^100 in terms of I, A, and A^2. These methods can significantly reduce the complexity of the multiplication involved. Exploring these approaches will help achieve the desired result without extensive manual multiplication.
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hi guys...my teacher wants me to calculate A^100 of a 3*3 matrix by hand...i can't use MATLAB for this...how do i do it...i can't imagine multiplying 100 time...
help me
 
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(A^50)^2

But most likely this is a specific matrix, with interesting properties that make it easy to calculate power no matter how high.
 
Check if the matrix is diagonalizable or, if it isn't, use the Jordan form to write it as a sum of a diagonal plus nilpotent matrix.
 
thanks guys...will try all
 
Yet another way is to use the minimal polynomial to express A^100 in terms of I, A, A^2.
 
i actually did it by finding the eigen values of the matrix...
anyways thank u guys for responding
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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