Given a matrix A with complex entries, how do I find the invertible matrix P such that P^-1 * A * P is upper triangular? I have seen the proof of the fact that every matrix is similar to an upper triangular matrix, but the proof was by induction and so I don't think that it can be used to construct the matrix.
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Question about (upper) triangular matrices watch
- Thread Starter
- 08-04-2011 22:38
- 08-04-2011 22:59
The idea is that if you can find an eigenvector then the image of that eigenvector is going to be a multiple of itself, so choose that to be your first basis vector; then you have a column that looks like . Then you need to proceed to find linearly independent vectors such that for each , when you apply your matrix to it what you get is some linear combination of (i.e. and not ). Then the matrix must be upper-triangular with respect to the resulting basis.