Hi!

If I have the following matrix, call it B, (3x3 with entries separated by commas)

8, 12, 0

0, 8, 12

0, 0, 8

How can I find a matrix A such that A^3 = B?

Since B is not diagonalizable I have no idea how to approach this problem.

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- December 8th 2009, 11:54 AMVolcanicrainPowers of a matrix
Hi!

If I have the following matrix, call it B, (3x3 with entries separated by commas)

8, 12, 0

0, 8, 12

0, 0, 8

How can I find a matrix A such that A^3 = B?

Since B is not diagonalizable I have no idea how to approach this problem. - December 8th 2009, 02:18 PMqmech
Trial and Error gives:

2,1,-0.5

0,2,1

0,0,2

whose cube is the matrix you want. - December 9th 2009, 08:39 AMHallsofIvy
"Brute strength" works. Because B is "upper triangular", you know A will also be "upper triangular" and look for a solution of the form .

Now, it's not too hard to calculate that and then that

Set that equal to B and you have 6 equations to solve for a, b, c, d, e, and f. - December 9th 2009, 08:47 AMVolcanicrain
Thanks!

I had considered that before in my mind, but I wasn't sure if there wasn't an easier way.

But it really isn't so bad!

Thanks a lot!