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# Question about (upper) triangular matrices watch

1. 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.
2. 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.

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Updated: April 8, 2011
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