2. (1) Compute all eigenvalues and eigenvectors of the Cartan matrix 2 -1 C = -1 -1 0 -1 2 (2) Diagonalize C (i.e. find Q such that Q¬'CQ is diagonal). (3) Is C positive definite?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2.
(1) Compute all eigenvalues and eigenvectors of the Cartan matrix
2
-1
C =
-1
2
-1
-1
2
(2) Diagonalize C (i.e. find Q such that Q-'CQ is diagonal).
(3) Is C positive definite?
Transcribed Image Text:2. (1) Compute all eigenvalues and eigenvectors of the Cartan matrix 2 -1 C = -1 2 -1 -1 2 (2) Diagonalize C (i.e. find Q such that Q-'CQ is diagonal). (3) Is C positive definite?
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