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In the Jordan form of square matrix $A \longrightarrow T^{-1}AT = J$, $J$ needs to be upper bidiagonal; but should the upper diagonal be restricted to ones?.

The equations $Av_i = v_{i-1} + \lambda_iv_i $, where $v_i$ are the columns of $T$, result from the Jordan form and they establish the linear independence of $T$'s columns. Why cant we have $Av_i = 2v_{i-1} + \lambda_iv_i $ with upper diagonal being 2 or just any number.

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    Because that's not what the Jordan **canonical** form is. Are you asking whether such a matrix would be as simple to analyze as the Jordan form? Close, though if you look at the formulas for *powers* of the Jordan form you will see that the blocks have a very nice form, as do square roots and other matrices of interest. It's not clear that such would be the case with such a variant.2012-07-15
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    Ones and zeros.2012-07-15

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