3x3 Diagonalizable Matrices over GF(2)

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The discussion centers on finding the 8 diagonalizable 3x3 matrices over GF(2), where entries are limited to 0's and 1's. Participants clarify that diagonalizable matrices need not be symmetric and can have repeated eigenvalues, which complicates the count beyond the 8 diagonal matrices initially suggested. A program was created to determine that there are 168 invertible matrices and 58 diagonalizable matrices over GF(2). The conversation also touches on the nature of eigenvalues and the implications of diagonalizability in the context of linear algebra. Ultimately, the original poster realizes the need to focus on diagonal matrices rather than diagonalizable ones for their research.
  • #31
ArcanaNoir said:
They need not be invertible.



I'm confused about this, first you say the main diagonal can only have non-zero entries, but then you say the main diagonal can have 0's or 1's. Also, diagonalizable is not the same as diagonal, right?
IlikeSerena made a slight grammatical error.

He/she said "the main diagonal can only have non-zero entries". What he/she meant to say was "only the main diagonal can have non-zero entries". The position of the word "only" is crucial!
 
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  • #32
HallsofIvy said:
IlikeSerena made a slight grammatical error.

He/she said "the main diagonal can only have non-zero entries". What he/she meant to say was "only the main diagonal can have non-zero entries". The position of the word "only" is crucial!

thanks for the clarification :)
 

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