Matrix Toolbox

A C console program for working with matrices.
Supports: creation (manual/random), file I/O, addition, subtraction, multiplication, transpose, determinant, and inverse.

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Mathematical Background

Example (3×3 matrix)

$$ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} $$

Determinant:

$$ \det(A) = 0 $$

(Singular → no inverse exists)

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Example (2×2 matrix)

$$ B = \begin{bmatrix} 2 & 1 \\ 5 & 3 \end{bmatrix} $$

Determinant:

$$ \det(B) = (2 \cdot 3) - (5 \cdot 1) = 1 $$

Inverse:

$$ B^{-1} = \begin{bmatrix} 3 & -1 \\ -5 & 2 \end{bmatrix} $$

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Implemented Operations

• Addition / Subtraction

$$ (A \pm B)_{ij} = A_{ij} \pm B_{ij} $$

• Multiplication

$$ (AB)_{ij} = \sum_{k=1}^{n} A_{ik} , B_{kj} $$

• Transpose

$$ (A^T)_{ij} = A_{ji} $$

• Determinant & Inverse
  via Gaussian elimination with partial pivoting.

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Complexity

• Addition/Subtraction: $O(n^2)$
• Multiplication: $O(n^3)$
• Determinant/Inverse: $O(n^3)$

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Usage

Compile:

gcc -std=c11 -O2 -Wall -lm -o matrix matrix.c

Run:

./matrix

Console demo:

=== Matrix Toolbox ===
1) Create new matrix
2) Random matrix
...
> 2
Rows: 3
Cols: 3
Min: 0
Max: 10
Random matrix created:
  1.00  2.00  3.00
  4.00  5.00  6.00
  7.00  8.00  9.00

Determinant = 0