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**jax** +riangularize the operator T: C^3 --> C^3 given by T(x,y,z)= (x, yi, y+zi). Find the ordered basis B and the upper triangular matrix Mat(T, B ,B).

This is what I have so far, please let me know how it looks. Thanks!

Standard basis : (1,0,0)=(1,0,0)

(0,1,0)=(0, i, 1)

(0,0,1)=(0,0, i)

What do you mean with these weird equalities?? The 2nd and 3rd. ones are obviously false...

Take simply the standard basis $\displaystyle \left\{(1,0,0), (0,1,0), (0,0,1)\right\}$...

Apply i times the second row and add to the third.

Now I have (1,0,0)

(0, i, 0)

(0,1, i)

So the eigen values are {1,i}