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Lecture 48. Root Spaces
Автор: Yuly Billig
Загружено: 2024-04-01
Просмотров: 655
Описание:
0:00 Geometric and algebraic multiplicities of eigenvalues
5:10 Definition of a root space
8:19 Properties of root spaces
12:58 Three exercises on root spaces
15:10 Root Space Decomposition Theorem
26:20 Proof of the Root Space Decomposition Theorem
In this lecture, we introduce root spaces (generalized eigenspaces) for a linear operator. We prove the Root Space Decomposition Theorem for an operator on a complex finite-dimensional vector space.
This is a lecture in the "Linear Algebra" course for students specializing in mathematics.
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