MATH115 Lecture 27: lect115_27_f14
10 Oct 2015
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Tuesday, november 4 lecture 27 : diagonalizable matrices. Concepts: define diagonalizable n n matrix a, recognize that a matrix a is diagonalizable if the matrix a has n distinct, diagonalize simple 2 by 2 or 3 by 3 matrices. eigenvalues. 27. 1 theorem suppose a is an n n matrix with n distinct eigenvalues. Let x be the n n matrix whose columns are the n eigenvectors which are respectively associated to the n distinct eigenvalues of a matrix a. Given : suppose {v1, v2, , vn} are n distinct eigenvectors respectively associated to n distinct eigenvalues { 1, 2, , n}. Required to show : that a = [v1 v2 vn ] is invertible. Then one vector, say v1, is a linear combination of the others {v2, , vn}. If this set {v2, , vn} is not linearly independent we can reduce it to a smaller linearly independent set, say {v2, , vm}.
