feat(matrix): add QR decomposition algorithm using Gram-Schmidt process

[MD-Mushfiqur123]

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?

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 Java 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 Java naming conventions.
• All new algorithms have a URL in its comments that points to Wikipedia or another similar explanation.
• The build runs successfully with mvn clean verify.

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QR Decomposition (Gram-Schmidt Process)

Decomposes a matrix A into an orthogonal matrix Q and an upper triangular matrix R such that A = Q * R.

What This Adds

QRDecomposition.java - Main algorithm implementation:

• decompose() - Performs QR factorization using the Gram-Schmidt process
• Returns a QR object containing both Q (orthogonal) and R (upper triangular) matrices
• Validates input matrix using MatrixUtil.validateInputMatrix()
• Throws ArithmeticException for rank-deficient matrices

QRDecompositionTest.java - Unit tests:

• Tests for 2x2 and 3x3 matrix decomposition
• Verifies Q * R reconstruction equals original matrix
• Validates Q columns are orthonormal
• Confirms R is upper triangular
• Tests identity matrix decomposition
• Tests rank-deficient matrix rejection
• Tests null and empty matrix rejection

Algorithm

The Gram-Schmidt process orthogonalizes columns iteratively:

• For each column j, subtract projections onto previous orthogonal vectors
• Normalize to get j-th column of Q
• Store coefficients in R[i][j]

Time: O(mn^2) | Space: O(mn + n^2)

Reference

https://en.wikipedia.org/wiki/QR_decomposition

[codecov-commenter]

Codecov Report

❌ Patch coverage is 87.09677% with 8 lines in your changes missing coverage. Please review.
✅ Project coverage is 79.65%. Comparing base (4b8099c) to head (efecad4).

Files with missing lines	Patch %	Lines
...java/com/thealgorithms/matrix/QRDecomposition.java	87.09%	4 Missing and 4 partials ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #7427      +/-   ##
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+ Coverage     79.63%   79.65%   +0.01%     
- Complexity     7241     7263      +22     
============================================
  Files           800      801       +1     
  Lines         23608    23670      +62     
  Branches       4646     4659      +13     
============================================
+ Hits          18800    18854      +54     
- Misses         4055     4059       +4     
- Partials        753      757       +4     

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