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Is it true that any lower triangular square matrix on a field, is similar to an upper triangular matrix? (So defining a triangular linear tranformation is simpler).

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    $\begingroup$ Well, since any square matrix is similar to its transpose the answer is yes. $\endgroup$ – DonAntonio Dec 2 '13 at 12:52
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Yes, it is true. Just use similarity matrix

$$S = \begin{bmatrix} & & & 1 \\ & & 1 & \\ & \mathinner{\mkern1mu\raise1pt\hbox{.}\mkern2mu\raise4pt\hbox{.}} & & \\ 1 & & & \end{bmatrix}.$$

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