fix: correct matrix size validation and handle rectangular matrix operations

[hardikkaurani]

Describe your change

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

Problem & Context

1. Index error in _verify_matrix_sizes:
   In matrix/matrix_operation.py, _shape(matrix_a) + _shape(matrix_b) produces (rows_a, cols_a, rows_b, cols_b). The condition shape[0] != shape[3] or shape[1] != shape[2] inadvertently compared rows_a with cols_b and cols_a with rows_b. This caused valid addition and subtraction of identical rectangular (non-square) matrices (e.g., add([[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]])) to erroneously raise ValueError: operands could not be broadcast together with shape ((2, 3)), ((2, 3)).
2. Dimension check & UnboundLocalError in multiply():
   In multiply(), calling _verify_matrix_sizes was incorrect because matrix multiplication does not require operands to have identical shapes; it requires inner dimensions to match (cols_a == rows_b). Calling _verify_matrix_sizes rejected valid multiplications where rows_a != cols_b (e.g. multiplying a 2x3 matrix with a 3x4 matrix). Furthermore, passing non-matrix inputs caused an UnboundLocalError on cols instead of raising TypeError("Expected a matrix, got int/list instead") like add() and subtract().
3. ty warning on redundant condition in subtract():
   Calling and _verify_matrix_sizes(matrix_a, matrix_b) inside the if condition triggered ty's warning[redundant-condition]: A 2-element tuple is always truthy.

Changes Made

• In _verify_matrix_sizes(), corrected the condition to shape[0] != shape[2] or shape[1] != shape[3].
• In subtract(), invoked _verify_matrix_sizes(matrix_a, matrix_b) as a statement, matching add().
• In multiply(), compared inner dimensions cols_a == rows_b directly and raised TypeError when inputs are not matrices.
• Added doctests covering rectangular matrix addition, subtraction, and multiplication.
• Updated matrix/tests/test_matrix_operation.py to test rectangular matrices and corrected copy-pasted helper calls (matop.add -> matop.multiply in test_multiplication).

Verification

• uvx --with numpy pytest matrix/tests/test_matrix_operation.py matrix/matrix_operation.py --doctest-modules: 33 passed.
• uvx ty check matrix/matrix_operation.py: All checks passed (0 diagnostics, 0 warnings).
• uvx ruff check matrix/matrix_operation.py matrix/tests/test_matrix_operation.py: All checks passed.
• uvx ruff format --check matrix/matrix_operation.py matrix/tests/test_matrix_operation.py: Clean.

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.

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[hardikkaurani]

Hi @cclauss,

I've submitted this pull request to fix an index transposition in _verify_matrix_sizes() and correct the dimension checks in matrix/matrix_operation.py.

Quick overview of the fixes:

1. Rectangular matrix addition and subtraction:
   _shape(matrix_a) + _shape(matrix_b) produces (rows_a, cols_a, rows_b, cols_b). The check shape[0] != shape[3] or shape[1] != shape[2] inadvertently compared rows_a with cols_b and cols_a with rows_b, which caused valid addition and subtraction of identical rectangular matrices (such as two 2x3 matrices) to fail with ValueError. This is now corrected to shape[0] != shape[2] or shape[1] != shape[3].
2. Matrix multiplication dimension check & input handling:
   multiply() previously called _verify_matrix_sizes, which erroneously prevented multiplying matrices with distinct outer dimensions (e.g., 2x3 by 3x4). This now verifies inner dimensions cols_a == rows_b directly. In addition, passing invalid inputs to multiply() now raises TypeError consistently instead of raising an UnboundLocalError.
3. ty clean:
   Calling _verify_matrix_sizes as a statement in subtract() eliminates ty's warning[redundant-condition]: A 2-element tuple is always truthy.
4. Testing:
   Added doctests and updated matrix/tests/test_matrix_operation.py with rectangular test cases and fixed the test helper calls.

All 33 unit tests and doctests pass (uvx --with numpy pytest matrix/tests/test_matrix_operation.py matrix/matrix_operation.py --doctest-modules), ty check matrix/matrix_operation.py passes with 0 diagnostics, and ruff check/ruff format are completely clean.

Whenever you have a chance, could you please take a look? Thank you!