Fix Perron-Frobenius index nonemptiness#139
Open
A-M-Berns wants to merge 1 commit intoleanprover:mainfrom
Open
Fix Perron-Frobenius index nonemptiness#139A-M-Berns wants to merge 1 commit intoleanprover:mainfrom
A-M-Berns wants to merge 1 commit intoleanprover:mainfrom
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Fixes a statement issue in the Perron-Frobenius benchmark.
As currently stated, the theorem is false for
n = Empty. In that case,(0 : Matrix Empty Empty ℝ).IsIrreducibleis provable because the nonnegativity and strong-connectivity fields are vacuous. But the conclusion asks for aModule.End.HasEigenvector, andHasEigenvectorrequires the vector to be nonzero; no functionEmpty → ℝcan be nonzero.This PR adds
[Nonempty n], matching the intended finite nonempty matrix statement.Verified with: