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1. Let C denote the field of complex numbers. As with any field, we can consider vector spaces, linear
3. For their; (inflation, are magir choose arbitraryr matrix mpruaantatiaa. usuallyuse the standard basis, and do the same as what we did in the previcrusEIGI'CiSE. Ha hm we‘ll have [T13 = D and the set of minim: VH‘JSDI'S of Qis the Drdmed basis ,8 {3] It’s not diagn-nalizahlc since dim[Eg} is 1 but not 4. Hill -ll{.'| [-3) It’s not diagonalimhla since its dimisflc polynomial rims notsplit. ..1 [I [I l l {I{h]1t’sdiaganafissab1awithfl= u 1 0 me: u u 1. 1 l l l{:1} It’s diagnnalizahla 1with 13- (fl: 2 [I] and Q =(= l l —l)_[I[a ]| It’s diagonafimable with D: ( —1 i][f] 111’; tfiagnnaligahle with D— - [— 1':i] J 'I'J.T_ __J. L.-._-- -__:_ 11__1-__ 4.1.- -L-___J.__JT' L- d.L_ -1.-___|._ I. :. J.L_ I.
