MATOPS - Matrix Operations Calculator

Author: Anant Rajput
Version: 2.2.0
Last Updated: December 22, 2025

A comprehensive C program for performing essential matrix operations including multiplication, determinants, inverses, characteristic equations, eigenvalues, eigenvectors, and transpose operations. Features password protection and an intuitive menu-driven interface.

Features

Seven Matrix Operations: Multiplication, determinant calculation, matrix inversion, characteristic equations, eigenvalues, eigenvectors, and transpose
Password Protection: Secure login system with 5 attempt limit (default password: 12345)
Input Validation: Ensures valid dimensions and operation compatibility
Interactive Menu: User-friendly interface with clear operation selection
System Settings: View version, author, maintainer, and update information
Memory Efficient: Uses Variable Length Arrays (VLA) for dynamic allocation
Square Matrix Support: Specialized operations for 1×1, 2×2, and 3×3 matrices

Operations Supported

1. Matrix Multiplication

Multiplies two matrices of compatible dimensions
Validates that columns of Matrix A equal rows of Matrix B
Supports matrices of any valid size (limited by stack memory)

2. Determinant Calculation

Computes determinants for square matrices
Supports 1×1, 2×2, and 3×3 matrices
Uses standard cofactor expansion method

3. Matrix Inverse

Calculates inverse using the adjugate method
Supports 1×1, 2×2, and 3×3 matrices
Checks for singular matrices (determinant = 0)
Output in floating-point format with 2 decimal precision

4. Characteristic Equation

Derives the characteristic polynomial
Supports 2×2 and 3×3 matrices
Output format:
- 2×2: λ² - (trace)λ + det
- 3×3: λ³ - (trace)λ² + (sum of minors)λ - det

5. Eigenvalues

Calculates eigenvalues for 2×2 matrices
Uses quadratic formula from characteristic equation
Displays both eigenvalues (real roots)

6. Eigenvectors

Computes eigenvectors for 2×2 matrices
Displays vectors corresponding to each eigenvalue
Uses null space method

7. Transpose

Computes transpose for any matrix size
Swaps rows and columns
Supports both square and rectangular matrices

8. System Settings

View version number
View author information
View maintainer details
Check recent update date
Return to main menu

Prerequisites

C Compiler: GCC or any compiler supporting C99 standard
Math Library: Requires linking with math library (-lm flag)
Basic understanding of linear algebra concepts

Compilation

gcc matops.c -o matops -lm

Or explicitly with C99 standard:

gcc -std=c99 matops.c -o matops -lm

Note: The -lm flag links the math library required for sqrt() function.

Usage

Run the program:
```
./matops
```
Enter password: Default password is 12345 (5 attempts allowed)
Select an operation from the menu (0-8)
Enter matrix dimensions when prompted
Input matrix elements as requested
View results or error messages
Access System Settings (option 8) for program information

Examples

Example 1: Matrix Multiplication

WELCOME TO MATOPS
__________________
ENTER PASSWORD TO LOG IN: 12345

WELCOME TO MATOPS
__________________
CHOOSE OPERATIONS:
1. MATRIX MULTIPLICATION
...
ENTER YOUR CHOICE: 1

ENTER THE NUMBER OF ROWS OF MATRIX A: 2
ENTER THE NUMBER OF COLUMN OF MATRIX A: 3
ENTER THE NUMBER OF ROWS IN MATRIX B: 3
ENTER THE NUMBER OF COLUMN IN MATRIX B: 2

ENTER THE ELEMENTS OF MATRIX A:
1 2 3
4 5 6

ENTER THE ELEMENTS OF MATRIX B:
7 8
9 10
11 12

THE RESULT OF MULTIPLICATION OF MATRIX A AND MATRIX B IS:
58      64
139     154

Example 2: Determinant (3×3 Matrix)

ENTER YOUR CHOICE: 2
ENTER THE NUMBER OF ROWS OF MATRIX A: 3
ENTER THE NUMBER OF COLUMN OF MATRIX A: 3

ENTER THE ELEMENTS OF MAT A:
1 2 3
0 1 4
5 6 0

DETERMINANT OF MATRIX A IS: 1

Example 3: Matrix Inverse (2×2)

ENTER YOUR CHOICE: 3
ENTER THE NUMBER OF ROWS OF MATRIX A: 2
ENTER THE NUMBER OF COLUMN OF MATRIX A: 2

ENTER ELEMENTS OF MATRIX A:
4 7
2 6

INVERSE OF MATRIX A IS:
0.60    -0.70
-0.20    0.40

Example 4: Eigenvalues (2×2)

ENTER YOUR CHOICE: 5
ENTER THE NUMBER OF ROWS OF MATRIX A: 2
ENTER THE NUMBER OF COLUMN OF MATRIX A: 2

ENTER ELEMENTS OF MATRIX A:
3 1
1 3

EIGEN VALUE OF MATRIX A IS: 4.000000 and 2.000000

Example 5: Transpose

ENTER YOUR CHOICE: 7
ENTER THE NUMBER OF ROWS OF MATRIX A: 2
ENTER THE NUMBER OF COLUMN OF MATRIX A: 3

ENTER ELEMENTS OF MATRIX A:
1 2 3
4 5 6

THE TRANSPOSE OF THE MATRIX A IS:
1       4
2       5
3       6

Error Handling

The program validates and handles:

Zero Dimensions: Rejects matrices with zero rows or columns
Non-Square Matrices: For operations requiring square matrices (determinant, inverse, eigenvalues)
Incompatible Dimensions: For matrix multiplication (columns of A ≠ rows of B)
Singular Matrices: Detects when inverse doesn't exist (determinant = 0)
Unsupported Sizes: Provides clear messages for matrix sizes beyond current support
Password Protection: Locks after 5 failed login attempts
Invalid Menu Choices: Prompts for valid input (0-8)

Code Structure

main()
├── Password Authentication Loop
│   └── 5 attempts allowed
├── Menu Display
├── Choice Selection
└── Operation Branches
    ├── Matrix Multiplication (choice 1)
    ├── Determinant Calculation (choice 2)
    ├── Matrix Inverse (choice 3)
    ├── Characteristic Equation (choice 4)
    ├── Eigenvalues (choice 5)
    ├── Eigenvectors (choice 6)
    ├── Transpose (choice 7)
    └── System Settings (choice 8)
        ├── Version Number
        ├── Author
        ├── Maintainer
        └── Recent Update Date

Each operation includes:

Dimension input and validation
Matrix element input
Computation using appropriate algorithm
Formatted output display

Limitations

Matrix Size:

Multiplication/Transpose: Any valid size (limited by stack memory)
Determinant/Inverse: Up to 3×3 matrices
Characteristic Equation: 2×2 and 3×3 matrices only
Eigenvalues/Eigenvectors: Only 2×2 matrices

Data Types:

Integer input for most operations
Float output for inverse and eigenvalues
No support for complex numbers

Other Limitations:

Complex Numbers: Does not handle complex eigenvalues/eigenvectors
Numerical Precision: Subject to floating-point arithmetic limitations
Memory: VLA size limited by available stack memory
Password: Hardcoded (not user-configurable without recompilation)

Possible Enhancements

Support for larger matrices (4×4, 5×5, etc.)
User-configurable password system
Gaussian elimination for general matrix inversion
LU decomposition for improved determinant calculation
QR algorithm for eigenvalue computation of larger matrices
Complex eigenvalue/eigenvector support
Matrix addition and subtraction operations
File I/O for loading/saving matrices
Error tolerance settings for floating-point comparisons
Matrix rank calculation
Reduced row echelon form (RREF)
Singular Value Decomposition (SVD)
Save operation history
Export results to file

Contributing

Contributions are welcome! To contribute:

Fork the repository
Create a feature branch (git checkout -b feature/enhancement)
Commit your changes (git commit -m 'Add new feature')
Push to the branch (git push origin feature/enhancement)
Open a Pull Request

Please ensure your code:

Follows existing style conventions
Includes appropriate comments
Handles edge cases and errors
Has been tested with various inputs
Updates documentation as needed

License

This project is open-source under the MIT License.

Contact

Maintainer: Anant Rajput

For bug reports, feature requests, or contributions, please open an issue in the repository.

Note: Default password is 12345. Change it in the source code for security purposes in production use.

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