MA 35100 Lecture : MA 35100 - Lecture 38
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To diagonalize an nxh matrix a means to write it in the form a: qdq where is invertible and d is diagonal. Aan] i. e. aqi = x, qi for all i c i. e. Aan] i. e. aqi = x, qi for all i c i. e. go is a xi-eigenvector for a. Note: & invertible means its columns are a basis of du (of eigenvectors for al columns are linearly independent. So, writing a: qdq" is equivalent to saying [0 on3 is a basis of eigenvectors of a for th with eigenvectors corresponding to entries of. I could have put these in a different order, but must be consistent across & and b. Notice: a = pp for b: 90. If a diagonalizable with a. obc", then what is the. If d = [ [n], then bm =[*jm] ex. n =(59] Finde-values (solve det (a-xi) =0) and e-vectors for each x. If am (x) >i, find a basis (solve(a-xi(x =0)
