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Finding powers of a matrix?

OK, our book does a pretty poor job of covering this one topic, and I can't find it anywhere else on the web. How do you find the formula for the n-th power of a 2*2 matrix (where n is a positive integer). For example, I have the matrix -1 1 -16 7 How do I take it to the, say, 7th power without multiplying the d**n thing 7 times by itself?

Asked By: rahidz2003 - 4/6/2006
Best Answer - Chosen by Asker
Diagonalisation is the answer here. Not sure how this didn't turn up in a web search, as I found plenty of resources for it, but the idea is that you find a matrix that diagonalises your initial matrix, and this allows powers to be done trivially... More
Answered By: Ross B - 4/6/2006
Additional Answers (5)
2x2 to the seventh power
Answered By: charlesoflagro - 4/6/2006
 
2 start with,a 2 by 2 matrix is one with 2 columns and 2 rows.Remember rows are horizontal(like across the line) and columns are vertical(like down the line).In other words,a 2 by 2 matrix consist of 4 seperate numbers.e.g... More
Answered By: babzikay - 4/6/2006
 
if you go to www.quickmath.com You should get an answer of (-18225,5103) (-81648,22599)
Answered By: still_a_virgin81 - 4/6/2006
 
For a 2x2 matrix, the easiest way is probably by using the characteristic polynomial. Let A be your matrix. Then... More
Answered By: mathematician - 4/6/2006
 
Ross B and mathematician gave the most practical answers. I have one comment on this remark of yours, though... More
Answered By: Dan D - 4/6/2006
 

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