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[Linear Algebra]

1a) Let A be an n × n-matrix. Suppose that A has n eigenvectors linearly independent. v1, ..., vn associated with n eigenvalues λ1, ..., λn. If we denote by S the matrix whose column i is vi, and by D the diagonal matrix of eigenvalues, show that AS = SD. Hint: Express in matrix the equations Avi = viλi).
1b) Use the previous item to prove that if A has n eigenvectors linearly independent, then it is diagonalizable.

User Sks
by
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1 Answer

3 votes

Answer:

a is nxn

Explanation:

d the diagonal matrix

is the answers

User Dmytroy
by
8.8k points
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