Given that the the Jordan normal form of a matrix is,


How do you find the 'real' canonical form of the matrix?

  • $\begingroup$ You could get a real $2 \times 2$ block insted of the complex diagonal block. This would also give you real basis-vectors $\endgroup$ – Laray Mar 29 '17 at 8:09

Wubbish. There clearly is such a thing. Just replace the complex pair by the $2\times 2$ block below.


You can compare the block to the matrix:

$$\left[\begin{array}{rr}a&-b\\b&a\\\end{array}\right]$$ which can be used to represent arbitrary complex numbers $a+bi$ or $a-bi$ as long as you are consistent on which you are using for each new number / block.


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