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.
"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.