MATOPS - Matrix Operations Calculator

A comprehensive command-line matrix operations calculator written in C, featuring password protection, multiple matrix operations, and an intuitive menu-driven interface.

Author: Anant Rajput
Version: 4.2.1
Last Updated: December 27, 2025

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📋 Table of Contents

• Features
• Operations Supported
• Prerequisites
• Installation
• Usage
• Examples
• System Settings
• Error Handling
• Limitations
• Security
• Future Enhancements
• Contributing
• License
• Contact

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✨ Features

• 🔐 Password Protected: Secure login system with 5-attempt limit and persistent password storage
• 💾 Password Persistence: Password saved to password.txt file (default: 12345)
• 🔒 Password Recovery: Security question-based password recovery system
• 📊 Seven Matrix Operations: Complete suite of linear algebra operations
• ✅ Input Validation: Comprehensive dimension and compatibility checks
• 🎯 User-Friendly Interface: Clear, menu-driven navigation
• ⚙️ System Settings: Password management and program information
• 🧹 Screen Management: Clear screen functionality for better organization
• 💾 Memory Efficient: Dynamic memory allocation using VLAs
• 🔄 Session Persistence: Continue operations without restarting
• 🔒 Security Features: Forceful eviction after failed authentication attempts

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🔢 Operations Supported

1. Matrix Multiplication

• Multiplies two matrices A[r₁×c₁] and B[r₂×c₂]
• Validates compatibility (c₁ must equal r₂)
• Supports any valid matrix dimensions
• Input Type: Integer
• Output: Result matrix of size r₁×c₂

2. Determinant Calculation

• Computes determinants using cofactor expansion
• Supported sizes: 1×1, 2×2, 3×3
• Validates square matrix requirement
• Input Type: Integer
• Output: Integer determinant value

3. Matrix Inverse

• Calculates inverse using adjugate method
• Supported sizes: 1×1, 2×2, 3×3
• Checks for singular matrices (det = 0)
• Input Type: Float
• Output: Floating-point inverse (2 decimal places)

4. Characteristic Equation

• Derives characteristic polynomial using trace and determinant
• Supported sizes: 2×2, 3×3
• Input Type: Integer
• Output format:
  • 2×2: λ² - (trace)λ + det
  • 3×3: λ³ - (trace)λ² + (sum of minors)λ - det

5. Eigenvalues

• Calculates eigenvalues using quadratic formula
• Supported sizes: 2×2 only
• Handles real eigenvalues (complex eigenvalues display as NaN)
• Input Type: Integer
• Output: Both eigenvalues (floating-point)

6. Eigenvectors

• Computes eigenvectors corresponding to eigenvalues
• Supported sizes: 2×2 only
• Uses simplified formula: [a₁₂, λ - a₁₁]ᵀ
• Input Type: Integer
• Output: Two eigenvectors in column form

7. Transpose

• Swaps rows and columns
• Supported sizes: Any dimensions
• Input Type: Integer
• Output: Transposed matrix

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🛠️ Prerequisites

• C Compiler: GCC 4.8+ or any C99-compatible compiler
• Operating System: Linux/Unix (uses system("clear"))
• Math Library: Standard C math library (-lm flag required)
• Knowledge: Basic understanding of linear algebra
• File Permissions: Write access for password.txt file

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📦 Installation

Clone or Download

# If using git
git clone https://github.com/yourusername/matops.git
cd matops

# Or download the source file directly

Compile the Program

gcc matops.c -o matops -lm

Or with explicit C99 standard:

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

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

For Windows Users

Replace system("clear") with system("cls") in the source code before compiling, or add conditional compilation:

#ifdef _WIN32
    system("cls");
#else
    system("clear");
#endif

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🚀 Usage

Running the Program

./matops

First Run

On first run, the program will:

1. Create password.txt if it doesn't exist
2. Set default password to 12345
3. Display the login screen

Login

• Default Password: 12345
• Attempts Allowed: 5
• Password Recovery: Enter 101 to access password recovery
• Recovery Question: "What is the name of author?"
• Answer: anant rajput or ANANT RAJPUT (case-insensitive)

Main Menu Navigation

------------------
WELCOME TO MATOPS
------------------

CHOOSE OPERATIONS:
1. MATRIX MULTIPLICATION
2. DETERMINANT (upto 3 * 3 matrix)
3. INVERSE
4. CHARACTERSTIC EQUATION
5. EIGEN VALUE
6. EIGEN VECTOR
7. TRANSPOSE OF A MATRIX
8. SYSTEM SETTINGS
9. CLEAR SCREEN
0. EXIT

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📚 Examples

Example 1: Matrix Multiplication (2×3 × 3×2)

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
------------------------------------------------------------

Calculation:

A × B = [1×7 + 2×9 + 3×11    1×8 + 2×10 + 3×12]
        [4×7 + 5×9 + 6×11    4×8 + 5×10 + 6×12]
      = [58   64]
        [139  154]

Example 2: Determinant (3×3)

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
------------------------------

Calculation:

det(A) = 1(1×0 - 4×6) - 2(0×0 - 4×5) + 3(0×6 - 1×5)
       = 1(-24) - 2(-20) + 3(-5)
       = -24 + 40 - 15
       = 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
---------------------------

Calculation:

det(A) = 4×6 - 7×2 = 24 - 14 = 10

A⁻¹ = (1/10) × [ 6  -7]  = [0.60  -0.70]
               [-2   4]    [-0.20  0.40]

Example 4: Characteristic Equation (2×2)

ENTER YOUR CHOICE: 4

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

--------------------------------------
CHARATERSTIC EQUATION OF MATRIX A IS:
λ² - 6λ + 8
---------------------------------------

Explanation:

Trace = 3 + 3 = 6
det(A) = 3×3 - 1×1 = 8

Characteristic equation: λ² - (trace)λ + det = λ² - 6λ + 8

Example 5: 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
-------------------------------------

Calculation:

Characteristic equation: λ² - 6λ + 8 = 0

Using quadratic formula:
λ = (6 ± √(36 - 32))/2 = (6 ± 2)/2

λ₁ = 4, λ₂ = 2

Example 6: Transpose (2×3)

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
------------------------------------

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⚙️ System Settings

Access via main menu option 8:

---------------
SYSTEM SETTINGS
---------------
1. VERSION NUMBER
2. AUTHOR
3. MAINTAINER
4. RECENT UPDATE DATE
5. SUPPORTED MATRIX LIMITS
6. CHANGE PASSWORD
7. CLEAR SCREEN
8. RETURN TO PREVIOUS MENU
9. LOG OUT

System Settings Options

1. Version Number

Displays current version: 4.2.1

2. Author

Shows author information: ANANT RAJPUT

3. Maintainer

Displays maintainer: ANANT RAJPUT

4. Recent Update Date

Last updated: 27 . DECEMBER . 2025

5. Supported Matrix Limits

------------------------------------------------
SUPPORTED MATRIX LIMITS
------------------------------------------------
• Multiplication : Any size (A[r×c], B[c×k])
• Determinant    : Up to 3 × 3
• Inverse        : 1 × 1, 2 × 2, 3 × 3
• Eigen Values   : 2 × 2 , 3 × 3
• Eigen Vectors  : 2 × 2 only
• Transpose      : Any size
------------------------------------------------

6. Change Password

Security-Enhanced Password Change Process:

• Requires current password verification (3 attempts)
• New password must be entered twice for confirmation
• Password 101 is reserved for system commands and cannot be used
• Password saved to password.txt automatically
• Automatic FORCEFUL EVICTION after 3 failed verification attempts

Password Change Flow:

1. Enter current password for verification
2. If correct, enter new password
3. Confirm new password (must match)
4. Success message displayed
5. Password saved to file
6. New password takes effect immediately

Failed Attempt Handling:

• Attempts 1-2: Warning with remaining attempts displayed

  Password is INCORRECT, TRY AGAIN (Attempts left = X)
  

• Attempt 3: System logs you out for security

  Password is INCORRECT, NO MORE TRIES LEFT
  Commencing FORCEFUL EVICTION due to security reasons.....LOADING.....
  

Password Mismatch:

• If new password and confirmation don't match:

  Both input password are different. TRY AGAIN
  

• 3 attempts allowed for password confirmation

7. Clear Screen

Clears the terminal for better visibility using system("clear")

8. Return to Previous Menu

Returns to main operations menu without logging out

9. Log Out

Logged Out of the System Successfully.

Exits to login screen while keeping program running

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🛡️ Error Handling

The program validates and handles various error conditions:

Input Validation Errors

Error Type	Validation	User Feedback
Zero Dimensions	Rejects matrices with 0 rows/columns	"ROWS AND COLUMNS MUST BE GREATER THAN ZERO."
Non-Square Matrix	Validates square requirement for det/inverse/eigen/char.eq.	Operation-specific error messages
Incompatible Multiplication	Checks c₁ = r₂ for A×B	"SORRY! THE MULTIPLICATION OF THE MATRIX IS NOT POSSIBLE."
Singular Matrix	Detects det = 0 for inverse calculation	"INVERSE DOES NOT EXIST"
Unsupported Size	Clear messages for operations beyond limits	"ONLY 2X2 AND 3X3 MATRIX SUPPORTED", etc.

Authentication Errors

Error Type	Attempts Allowed	User Feedback
Login Failure	5 attempts	"INCORRECT PASSWORD. NUMBER OF ATTEMPST LEFT = X"
Final Login Attempt	After 5th failure	"INCORRECT PASSWORD. NO MORE ATTEMPTS LEFT" → Program exits
Password Recovery Failure	1 attempt	"Failed to retrive password.commencing FORCE EVICTION."
Password Change Verification	3 attempts	"Password is INCORRECT, TRY AGAIN (Attempts left = X)"
Password Change Final Failure	After 3rd failure	"FORCEFUL EVICTION" → Logged out

Menu Errors

Error Type	Valid Range	User Feedback
Invalid Main Menu Choice	0-9	"INVALID RESPOSE (X). VALID RESPONSE = 0 - 9"
Invalid Settings Choice	1-9	"Invalid Response Detected (X). Valid response = (1 - 6)"

---

⚠️ Limitations

Matrix Size Constraints

Operation	Supported Sizes	Algorithm	Note
Multiplication	Any (memory limited)	Standard algorithm	Limited by stack size
Determinant	1×1, 2×2, 3×3	Cofactor expansion	Analytical formulas
Inverse	1×1, 2×2, 3×3	Adjugate method	Uses determinant
Characteristic Equation	2×2, 3×3	Analytical formulas	Trace & determinant based
Eigenvalues	2×2 only	Quadratic formula	Real eigenvalues only
Eigenvectors	2×2 only	Simplified formula	Based on eigenvalues
Transpose	Any	Direct computation	No limitation

Technical Limitations

• Complex Numbers: No support for complex eigenvalues/eigenvectors

  • Complex eigenvalues display as nan (Not a Number)
  • No user-friendly warning provided

• Data Types:

  • Matrix multiplication, determinant, characteristic equation: Integer input/output
  • Inverse: Float input/output (2 decimal precision)
  • Eigenvalues/eigenvectors: Integer input, float output

• Precision: Standard floating-point limitations

  • Uses float for inverse calculation
  • Uses double internally for sqrt() calculations
  • Output limited to 2 decimal places

• Memory:

  • VLA (Variable Length Array) size limited by available stack memory
  • Large matrices may cause stack overflow
  • No dynamic heap allocation used

• Platform:

  • system("clear") command is Unix/Linux specific
  • Windows requires modification to system("cls")

• Password Security:

  • Password stored in plain text in password.txt
  • File permissions not explicitly set
  • No encryption applied

• File Handling:

  • If password.txt is corrupted, defaults to 12345
  • No backup password mechanism
  • File must be writable in current directory

Known Issues

1. Complex Eigenvalues: When a 2×2 matrix has complex eigenvalues (discriminant < 0), sqrt() of negative number produces nan without explanation

2. Input Validation: No validation for non-numeric input

   • Entering letters causes undefined behavior
   • Program may crash or produce garbage values

3. Typos in Output:

   • "ATTEMPST" instead of "ATTEMPTS"
   • "characteric" instead of "characteristic"
   • "MARRIX" instead of "MATRIX"
   • "retrive" instead of "retrieve"

4. Password File Security: Plain text password storage is a security risk

5. No Confirmation: Exit (option 0) doesn't ask for confirmation

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🔐 Security

Security Considerations

⚠️ Important Security Notes:

1. Password Storage:

   • Passwords stored in plain text in password.txt
   • Not suitable for sensitive environments
   • For educational/personal use only

2. File Permissions:

   • password.txt created with default permissions
   • Recommend setting chmod 600 password.txt on Unix systems

3. Input Validation:

   • Limited validation of user input
   • Malicious input may cause crashes
   • Do not expose to untrusted users

4. Buffer Security:

   • VLA usage may cause stack overflow
   • No bounds checking on very large matrices

Password Recovery

• Recovery Code: Enter 101 at the login prompt
• Security Question: "What is the name of author?"
• Correct Answers: anant rajput or ANANT RAJPUT (case-insensitive)
• Failed Recovery: One attempt only, followed by immediate "FORCE EVICTION"

Security Best Practices

If using in any production or shared environment:

1. Change Default Password Immediately

   Default: 12345 → Change via System Settings (8 → 6)
   

2. Secure the Password File

   chmod 600 password.txt  # Unix/Linux

3. Run with Limited Privileges

   • Don't run as root/administrator
   • Use dedicated user account

4. Monitor for Unusual Behavior

   • Check for unexpected file access
   • Monitor program crashes

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🔮 Future Enhancements

High Priority

• Complex Number Support

  • Handle complex eigenvalues and eigenvectors
  • Display in a+bi format
  • Proper mathematical representation

• Larger Matrix Support

  • Extend determinant calculation to n×n matrices
  • Implement LU decomposition for inverse
  • QR algorithm for eigenvalues of larger matrices

• Input Validation

  • Handle non-numeric input gracefully
  • Validate input ranges
  • Add input sanitization

• Cross-Platform Compatibility

  • Automatic detection of OS
  • Use appropriate clear screen command
  • Portable file paths

• Enhanced Security

  • Encrypt password in file
  • Use secure password hashing
  • Add password strength requirements
  • Implement session timeouts

Medium Priority

• Additional Operations

  • Matrix addition and subtraction
  • Scalar multiplication and division
  • Matrix exponentiation
  • Rank calculation
  • RREF (Reduced Row Echelon Form)
  • Trace as separate operation
  • Norm calculations (L1, L2, infinity)

• Gaussian Elimination

  • Solve systems of linear equations
  • General solution finding
  • Pivoting strategies

• Advanced Decompositions

  • LU decomposition
  • QR decomposition
  • Cholesky decomposition
  • SVD (Singular Value Decomposition)

Low Priority

• File I/O

  • Import matrices from CSV/text files
  • Export results to files
  • Save calculation history

• GUI Version

  • GTK+ interface for Linux
  • Qt for cross-platform
  • Web-based interface

• Code Quality

  • Refactor into separate functions
  • Improve error handling
  • Add comprehensive comments
  • Unit testing framework

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🤝 Contributing

Contributions are welcome! Here's how you can help improve MATOPS:

How to Contribute

1. Fork the repository

   git clone https://github.com/yourusername/matops.git

2. Create a feature branch

   git checkout -b feature/amazing-feature

3. Make your changes

   • Write clean, readable code
   • Follow existing code style
   • Add comments for complex logic

4. Test thoroughly

   • Test with various inputs
   • Check edge cases
   • Verify no memory leaks

5. Commit your changes

   git commit -m 'Add amazing feature: detailed description'

6. Push to the branch

   git push origin feature/amazing-feature

7. Open a Pull Request

   • Provide clear description
   • Reference any related issues
   • Include screenshots if applicable

Contribution Guidelines

Code Style

• Indentation: 4 spaces (no tabs)
• Braces: K&R style

  if (condition) {
      // code
  }

• Naming:
  • Variables: snake_case
  • Functions: snake_case
  • Constants: UPPER_CASE
• Comments: Clear and concise

What to Contribute

Bug Fixes:

• Fix typos in output messages
• Correct calculation errors
• Fix memory issues
• Improve error handling

New Features:

• Add new matrix operations
• Implement larger matrix support
• Add complex number handling
• Create file I/O functionality

Documentation:

• Improve README
• Add code comments
• Create tutorials
• Write examples

Testing:

• Write test cases
• Report bugs
• Suggest improvements
• Validate calculations

Testing Checklist

Before submitting a pull request, ensure:

• Code compiles without warnings

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

• All operations work correctly
• Edge cases handled (zero matrices, singular matrices, etc.)
• No memory leaks (test with valgrind if possible)
• Error messages are clear
• Documentation updated
• Code follows style guidelines

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📄 License

This project is licensed under the MIT License.

MIT License

Copyright (c) 2025 Anant Rajput

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

What This Means

✅ You CAN:

• Use the software for commercial purposes
• Modify the software
• Distribute the software
• Use the software privately
• Sublicense the software

❌ You CANNOT:

• Hold the author liable
• Expect warranty or guarantee

📋 You MUST:

• Include the license and copyright notice
• State changes made to the code

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📞 Contact

Author & Maintainer: Anant Rajput

Get in Touch

• GitHub Issues: Report bugs or request features
• Pull Requests: Contribute code
• Version: 4.2.1
• Last Updated: December 27, 2025

Support

If you find this project helpful:

• ⭐ Star the repository
• 🐛 Report bugs
• 💡 Suggest features
• 🤝 Contribute code
• 📢 Share with others

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🙏 Acknowledgments

• Mathematical Foundation: Standard linear algebra algorithms and formulations
• Educational Purpose: Built to help students understand matrix operations
• Open Source Community: Thanks to all contributors and users for feedback
• C Programming: Inspired by the simplicity and power of C language
• Learning Resource: Designed as both a tool and a learning reference

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📊 Project Statistics

Metric	Value
Current Version	4.2.1
Development Status	Active
Last Updated	December 27, 2025
Lines of Code	~750
Language	C (C99 standard)
License	MIT
Stability	Stable (Production Ready)
Platforms	Linux/Unix (Windows compatible with modifications)

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⚠️ Important Notes

⚠️ Security Warning

The default password is 12345. For any shared or production environment, change the password immediately via System Settings (Option 8 → 6). The password is stored in plain text in password.txt and is not encrypted.

💻 Platform Compatibility

This program uses system("clear") which is Unix/Linux specific.

Windows users must:

1. Replace system("clear") with system("cls")
2. Recompile the program

OR use:

#ifdef _WIN32
    system("cls");
#else
    system("clear");
#endif

💾 Memory Limitations

Large matrices may cause stack overflow due to VLA usage.

Recommendations:

• Keep matrix dimensions reasonable (<100×100)
• For very large matrices, consider implementing heap allocation
• Monitor system memory during operations

📁 File Requirements

The program needs write access to create and modify password.txt in the current directory.

Ensure:

• Current directory is writable
• Sufficient disk space available

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Made with ❤️ for Linear Algebra Students

MATOPS - Making Matrix Operations Simple and Accessible