Question

How would one diagonalize a complex matrix under congruence? Please provide an example if possible, thank you in advance.

Answer 1

Tot i ralli ain 1 : ' be an nxn inamin lani ..ann . . which is diagonalizable. 5 dv ., dt's a all the distinct e-ndues that occurs in the decompositions of the minimal polynomial of A. cet El is the eigenspace for the evolua ty į di a dim" ( Exi) : o Edisine loomine ut {wi, ---, vees basis for i - Tate pott, a voi Take paloi vam omogos ,,, be the matrin , pis non matrn since .. each Now, EiRM p'ap - 4 e 'AP diagonal y 1 with each ais occurs' most its T algebraic multiplicity = tinti Take n=2 . Take m= 2. AA ] complean madanion wal l 22 det (A-18) = 11 IL-ivel det (A-AD) –0'-) zo -)dzki

1 = alottino =) Il are the t value of A: Beyo hut usm eti Ang lova (A - ) v=0. Tali Test al - L ? ) pivni Live - 650s-iną = 425) V = ivez. - Take 82=1 =19= inv=(1,1). Tet - 14,vid ES & Av=-1-0 . =) (Attlu . [**][][:] Mting 20 =) v = will ! Take V.2E-1 val. aiva (1- ا = ( Tale po [ilo Wi] = [1 : p'ap = 1:0) diagonal. ...