Matrix Operations – Linear Algebra in C++

C++17 implementation of a Matrix class providing core linear algebra operations with robust error handling.

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Features

• Matrix addition and multiplication
• Matrix–vector multiplication
• Transpose
• Determinant (recursive cofactor expansion, small matrices)
• Element access via operator()(i, j)
• Exception handling (std::invalid_argument, std::out_of_range)
• Floating-point comparison with epsilon (1e-9)

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Project Structure

.
├── include/Matrix.h  
├── src/  
│   ├── Matrix.cpp  
│   ├── main.cpp  
│   ├── examples.cpp  
│   ├── tests.cpp  
│   ├── tests_extended.cpp  
│   └── benchmark.cpp  
├── Makefile  
└── architecture.drawio  

architecture.drawio provides a visual overview of the compilation pipeline and data flow.

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Compilation

Using Makefile

make              # Build project
make run          # Run main demo
make run-examples # Run additional examples
make test         # Run basic test suite (9 tests)
make bench        # Run performance benchmark
make clean        # Remove build files

Manual Compilation

g++ -std=c++17 -Wall -Wextra -Wpedantic -Wconversion \
-Iinclude src/Matrix.cpp src/main.cpp -o matrix_program

Extended Tests (19 tests)

g++ -std=c++17 -Wall -Wextra -Iinclude obj/Matrix.o \
src/tests_extended.cpp -o bin/tests_extended

./bin/tests_extended

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Implementation Details

• Storage: std::vector<double> (row-major layout)
• Determinant: recursive cofactor expansion
• Matrix multiplication: optimized i-k-j loop ordering
• Strict dimension validation
• Full exception safety for invalid operations

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Validation

• Compiles with strict flags (-Wall -Wextra -Wpedantic -Wconversion)
• C++17 compliant
• Zero warnings
• All tests passing

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