Can a Matrix Have Multiple Eigenbases?

  • Level: Undergrad 
  • Thread starter Niles
  • Start date
  • Tags Tags
    Multiple
2 replies · 3K views · last reply
Niles
Messages
1,834
Reaction score
0
Hi guys

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


Niles.
 

Discussion

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.
 

Similar threads

Undergrad How can a Markov process be reversible and have multiple eigenvalues equal to 1?
  • Mentz114
  • · Replies 12 ·
  • Linear and Abstract Algebra
Replies
12
Undergrad Can a Hermitian matrix have complex eigenvalues?
  • SeM
  • · Replies 4 ·
  • Linear and Abstract Algebra
Replies
4
Undergrad Can a matrix have both zero and non-zero eigenvalues?
  • Kubilay Yazoglu
  • · Replies 8 ·
  • Linear and Abstract Algebra
Replies
8
Undergrad Can a matrix with repeated eigenvalues be diagonalizable?
  • kostoglotov
  • · Replies 2 ·
  • Linear and Abstract Algebra
Replies
2
Can an eigenvalue have multiple eigenvectors?
  • wown
  • · Replies 4 ·
  • Calculus and Beyond Homework Help
Replies
4
Graduate How Can a Symmetric Matrix Have 2 Eigenvectors with Only 1 Eigenvalue?
  • jakey
  • · Replies 4 ·
  • Linear and Abstract Algebra
Replies
4
Undergrad Can a 2×2 matrix have complex eigenvalues?
  • Cygni
  • · Replies 8 ·
  • Linear and Abstract Algebra
Replies
8
Graduate Can a matrix A be decomposed if it doesn't have n distinct eigenvalues?
  • JanClaesen
  • · Replies 1 ·
  • Linear and Abstract Algebra
Replies
1
Undergrad Can a design matrix have any form, or are there restrictions?
  • mikeph
  • · Replies 2 ·
  • Set Theory, Logic, Probability, Statistics
Replies
2
Can a matrix have two different inverses?
  • trojansc82
  • · Replies 21 ·
  • Calculus and Beyond Homework Help
Replies
21