The rank of a matrix = the number of non-zero eigenvalues of the matrix!
So you can either use the top eigenvalues to count the non-zeros, or you can use the fact that an n×n matrix always has n eigenvalues to determine the number of non-zero eigenvalues by counting the bottom zero-eigenvalues.
Also for more detail on the “getting hessian eigenvalues without calculating the full hessian” thing, I’d really recommend Johns explanation in this linear algebra lecture he recorded.
Thanks for this! I misinterpreted Lucius as saying “use the single highest and single lowest eigenvalues to estimate the rank of a matrix” which I didn’t think was possible.
Counting the number of non-zero eigenvalues makes a lot more sense!
The rank of a matrix = the number of non-zero eigenvalues of the matrix! So you can either use the top eigenvalues to count the non-zeros, or you can use the fact that an n×n matrix always has n eigenvalues to determine the number of non-zero eigenvalues by counting the bottom zero-eigenvalues.
Also for more detail on the “getting hessian eigenvalues without calculating the full hessian” thing, I’d really recommend Johns explanation in this linear algebra lecture he recorded.
Thanks for this! I misinterpreted Lucius as saying “use the single highest and single lowest eigenvalues to estimate the rank of a matrix” which I didn’t think was possible.
Counting the number of non-zero eigenvalues makes a lot more sense!