Fix definition of primitive matrix and clarify Hamilton matrix reference #584
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Thanks @Nanakjoth for contribution! I just pushed some minor updates to the PR. |
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thanks @Nanakjoth and @HumphreyYang @Nanakjoth here is the documentation for the syntax on internal references for jupyter-book |
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Pull Request Overview
This pull request refines the definition of a primitive matrix and clarifies the reference to Hamilton’s transition matrix.
- Updates the primitive matrix condition to state that A^k is everywhere positive for some k.
- Changes the reference for the Hamilton matrix to use a reStructuredText reference pointing to mc_eg2.
Comments suppressed due to low confidence (1)
lectures/eigen_II.md:395
- [nitpick] To fully align with the PR description and avoid any ambiguity with Hamiltonian matrices from physics, consider updating the reference text to explicitly say 'Hamilton’s transition matrix'.
So Perron-Frobenius theorem explains why both {ref}`Imam and Temple matrix <mc_eg3>` and {ref}`Hamilton matrix <mc_eg2>` converge to a stationary distribution, which is the Perron projection of the two matrices
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| $A$ here is also a primitive matrix since $A^k$ is everywhere nonnegative for $k \in \mathbb{N}$. | |||
| $A$ here is also a primitive matrix since $A^k$ is everywhere positive for some $k \in \mathbb{N}$. | |||
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[nitpick] The updated definition appears correct; however, consider explicitly stating 'strictly positive' to align precisely with the standard mathematical definition of a primitive matrix.
| $A$ here is also a primitive matrix since $A^k$ is everywhere positive for some $k \in \mathbb{N}$. | |
| $A$ here is also a primitive matrix since $A^k$ is strictly positive for some $k \in \mathbb{N}$. |
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This PR fixes two minor issues referenced in #576:
Primitive matrix definition : Updated the condition to say$A^k$ is positive for some $k \in \mathbb{N}$ , which is the correct definition of a primitive matrix.
Hamilton matrix: Replaced the misleading term "Hamilton matrix" with "Hamilton’s transition matrix (
mc_eg2)" to avoid confusion with Hamiltonian matrices in physics.I hope this fix was helpful, Happy to make any changes if needed — just let me know.