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November 10th, 2006 ~ Posted in: Mathematics

It’s known that every square matrix is unitarily similar to an upper triangular matrix: $A \in \C^{n \times n} \Rightarrow \exists Q, T: A = QTQ^\star$ . Prove, using linear algebra, that this decomposition cannot in general be computed with a finite number of basic matrix operations (mult, add).

This result is known, but I believe only as a corollary of a theorem in another branch of mathematics.

Mathematics ~

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