Fix mypy errors in lu_decomposition.py

[tianyizheng02]

Describe your change:

• Fixed type hints in lu_decomposition.py to resolve mypy errors (see mypy produces errors when run on its own #8070)
• Added explanation of LU decomposition
• Added doctests to handle different cases in which an LU decomposition does or doesn't exist

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the commit message contains Fixes: #{$ISSUE_NO}.

[algorithms-keeper]

Multiple Pull Request Detected

@tianyizheng02, we are extremely excited that you want to submit multiple algorithms in this repository but we have a limit on how many pull request a user can keep open at a time. This is to make sure all maintainers and users focus on a limited number of pull requests at a time to maintain the quality of the code.

This pull request is being closed as the user already has an open pull request. Please focus on your previous pull request before opening another one. Thank you for your cooperation.

User opened pull requests (including this one): #8076, #8075, #8073, #8065

[tianyizheng02]

bruh

I thought the limit was 5 💀