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Lecture 40. Linear Independence of Eigenvectors
Автор: Yuly Billig
Загружено: 2024-03-03
Просмотров: 278
Описание:
0:00 Criterion for diagonalization of a matrix
8:01 Stronger form of the diagonalization criterion
10:03 Lemma on vector equations
15:53 Proposition on the sum of eigenvectors
22:12 Theorem on linear independence of eigenvectors
34:42 Example of a non-diagonalizable matrix
In this lecture, we prove that eigenvectors corresponding to distinct eigenvalues are linearly independent. As a corollary, we obtain a theorem stating that an n x n matrix is diagonalizable if and only if the sum of dimensions of its eigenspaces is equal to n.
This is a lecture in the "Linear Algebra" course for students specializing in mathematics.
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