Corollary. Let A e M,(F). Assume that its characteristic polynomial is a product of linear polynomials. Then there exists a Jordan matrix J and an invertible matrix C such that A = CJC¯!. I'm confused...

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Corollary. Let A e M,(F). Assume that its characteristic polynomial is a product of linear<br>polynomials. Then there exists a Jordan matrix J and an invertible matrix C such that<br>A = CJC¯!.<br>I'm confused on how to show that J and<br>C exist to satisfy the equation. Any<br>clarification here would be greatly<br>appreciated.<br>

Extracted text: Corollary. Let A e M,(F). Assume that its characteristic polynomial is a product of linear polynomials. Then there exists a Jordan matrix J and an invertible matrix C such that A = CJC¯!. I'm confused on how to show that J and C exist to satisfy the equation. Any clarification here would be greatly appreciated.

Jun 04, 2022

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Corollary. Let A e M,(F). Assume that its characteristic polynomial is a product of linear polynomials. Then there exists a Jordan matrix J and an invertible matrix C such that A = CJC¯!. I'm confused...

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