Matrix Toolkit

Matrix Toolkit offers classroom-friendly matrix calculations that keep arithmetic exact through Python's fractions.Fraction. The core logic lives in a reusable package, and the interactive command line interface is in Portuguese, while all documentation stays in English.

Features

Basic Operations

• Addition, subtraction, scalar multiplication – Standard matrix arithmetic
• Matrix multiplication – Standard product A × B
• Hadamard product – Element-wise multiplication A ⊙ B
• Matrix power – Raise matrices to integer powers (including A⁻¹)
• Transpose – Flip rows and columns

Determinant and Inverse

• Determinant – Recursive Laplace expansion
• Cofactor matrix – Matrix of cofactors
• Adjugate – Transpose of cofactor matrix
• Inverse – Via adjugate method with singularity checks
• Minor and cofactor – Individual (i,j) minor and cofactor

Matrix Reduction

• RREF – Reduced Row Echelon Form with step-by-step log
• LU Decomposition – Factor A = L × U (without pivoting)

Linear Systems

• Solve Ax = b – Gaussian elimination with step-by-step display
• Rank – Number of linearly independent rows/columns
• Nullity – Dimension of null space (cols - rank)

Matrix Properties

• Trace – Sum of diagonal elements
• Diagonal extraction – Get main diagonal as list
• Property checks: symmetric, diagonal, identity, zero, upper/lower triangular

Matrix Generators

• Identity matrix – Create I_n
• Zero matrix – Create m×n zero matrix

Norms

• Frobenius norm – √(sum of squared entries)

Additional Utilities

• Submatrix extraction – Extract rectangular regions
• Concatenation – Horizontal and vertical matrix joining

Core Features

• Exact arithmetic via fractions.Fraction; no third-party dependencies
• Interactive CLI in Portuguese with colored output and categorized menu
• Step-by-step display for educational purposes

Requirements

• Python 3.8 or newer; standard library only.

Usage (CLI in Portuguese)

Run the unified menu-driven CLI:

python scripts/matrix_cli.py
# or
python -m matrix_toolkit.cli

The CLI features:

• Categorized menu with 19 operations organized into 6 groups
• Colored output (ANSI) for better readability (auto-disabled if not a TTY)
• Step-by-step display for RREF, LU decomposition, and system solving
• Help system with input examples and operation descriptions
• Fraction support – Enter values like 1/2, -3/4 directly

Available categories:

1. Operacoes Basicas – Sum, subtract, scalar multiply, matrix multiply, Hadamard, power
2. Estrutura e Propriedades – Transpose, trace, diagonal, property checks
3. Determinante e Inversa – Determinant, inverse with cofactors
4. Reducao e Decomposicao – RREF, LU decomposition
5. Sistemas Lineares e Posto – Solve Ax=b, rank/nullity
6. Geradores e Normas – Identity, zero matrix, Frobenius norm

Legacy-style entry points remain for single tasks:

• python scripts/matriz_fera.py – RREF with printed row operations.
• python scripts/matriz_inversa_cofatores.py – Determinant, cofactors, adjugate, and inverse.

Using the library in Python code

from matrix_toolkit import (
    add_matrices, determinant, inverse, trace, rank,
    identity_matrix, is_symmetric, lu_decomposition,
    solve_system, matrix_power, rref
)

a = [[1, 2], [3, 4]]
b = [[2, 0], [1, 2]]

# Basic operations
sum_ab = add_matrices(a, b)
det_a = determinant(a)
inv_a = inverse(a)  # raises ValueError if singular

# New operations
tr = trace(a)                    # Sum of diagonal: 1 + 4 = 5
r = rank(a)                      # Matrix rank
I3 = identity_matrix(3)          # 3x3 identity
sym = is_symmetric(a)            # False
L, U = lu_decomposition(a)       # A = L × U
a_squared = matrix_power(a, 2)   # A²
reduced = rref(a)                # Row echelon form

# Solve linear system Ax = b
A = [[2, 1], [1, 3]]
b = [[5], [10]]
x = solve_system(A, b)           # Solution vector

All functions accept any numeric input coercible to Fraction and perform validation (shape checks, square requirements, etc.).

Repository Structure

README.md
LICENSE
matrix_toolkit/
  __init__.py          # Package exports
  cli.py               # Portuguese CLI with colored menu
  interactive.py       # Input/output helpers (Portuguese prompts)
  operations.py        # Pure matrix operations built on Fraction
scripts/
  matrix_cli.py                 # Entry point for the CLI menu
  matriz_fera.py                # RREF demo script
  matriz_inversa_cofatores.py   # Inverse demo script

License

This project is distributed under the MIT License. See LICENSE for details.