feat: Add LU decomposition algorithm for matrices using Doolittle's algorithm

[Raghu0703]

Description

This PR implements the LU decomposition algorithm for square matrices as requested in issue #6833.

Changes

• Implements LU decomposition using Doolittle's method
• Decomposes square matrix A into L (lower) and U (upper) triangular matrices
• Includes comprehensive test cases with edge case handling
• Time complexity: O(n³), Space complexity: O(n²)
• Resolves #6833

Algorithm Details

• Purpose: Decomposes a square matrix A into L × U where:
  • L is a lower triangular matrix with 1s on diagonal
  • U is an upper triangular matrix
• Use cases: Solving linear equations, computing determinants, finding matrix inverses
• Method: Doolittle's algorithm
• Time Complexity: O(n³)
• Space Complexity: O(n²)

Testing

• ✅ Basic 3x3 matrix decomposition (from issue example)
• ✅ Identity matrix decomposition
• ✅ 2x2 matrix decomposition
• ✅ Non-square matrix error handling
• ✅ Empty matrix error handling
• ✅ Singular matrix error handling

Checklist

• [x] I have read CONTRIBUTING.md.
• [x] This pull request is all my own work -- I have not plagiarized it.
• [x] All filenames are in PascalCase.
• [x] All functions and variable names follow Java naming conventions.
• [x] All new algorithms have a URL in their comments that points to Wikipedia or other similar explanations.
• [x] All new code is formatted with clang-format -i --style=file path/to/your/file.java

Closes #6833