Can a Matrix Have Multiple Eigenbases?

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A matrix can have multiple eigenbases, as the eigenbasis is not unique. In inner product spaces, the eigenbasis is unique up to orthonormalization. For the identity matrix and its scalar multiples, every basis qualifies as an eigenbasis. This highlights the flexibility in choosing eigenbases for certain matrices. Understanding these concepts is essential for advanced linear algebra applications.
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Hi guys

Is it possible for a matrix to have more than one eigenbasis?


Niles.
 
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The eigenbasis isn't unique.

I would say the eigenbasis is unique up to orthonormalization in inner product spaces.
 
Niles said:
Hi guys

Is it possible for a matrix to have more than one eigenbasis?


Niles.

For the identity matrix and its scalar multiples every basis is an eigen basis.
 

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