Eigenvalue question

  • Thread starter cragar
  • Start date
  • #1
2,544
2
Can I have a matrix that has an uncountable number of eigenvalues?
If the matrix was infinite.
And also can I have a matrix with a countable number of rows and an uncountable number of
columns?
 

Answers and Replies

  • #2
22,089
3,285
Sure, you can have that. But we often don't speak of "infinite dimensional matrix" anymore, but rather of a linear operator.
 
  • #3
2,544
2
Ok thanks for your answer. What about my second question?
Can I have a matrix with a countable number of rows and an uncountable number of
columns?
 
  • #4
22,089
3,285
The yes was to both questions.
 
  • #5
2,544
2
ok thanks. Are there any other crazy interesting properties of infinite matrices?
 
  • #6
22,089
3,285
The craziest property, I think, is that infinite matrices don't need to be continuous. This is quite a serious defect, since discontinuous linear maps are not so interesting.
 
  • #7
428
1
a matrix with countably many rows and uncountably many columns might be a linear map from functions to sequences.
 

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