Matrix Calculator

What is a Matrix Calculator?

A matrix calculator is a tool that performs operations on matrices, which are rectangular arrays of numbers arranged in rows and columns. Matrices are fundamental in linear algebra and have applications in various fields including computer graphics, physics, and data analysis.

This calculator supports basic matrix operations including addition, subtraction, multiplication, determinant calculation, and finding inverses for 2x2 matrices. It provides step-by-step solutions and handles both real and complex numbers.

Matrix Operations and Formulas

Common matrix operations include:

• Addition: (A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ
• Subtraction: (A - B)ᵢⱼ = Aᵢⱼ - Bᵢⱼ
• Multiplication: (AB)ᵢⱼ = Σₖ AᵢₖBₖⱼ
• Determinant: For 2x2 matrix: |A| = ad - bc
• Inverse: A⁻¹ = (1/|A|) * adj(A)

Example Calculation

Let's calculate the product of two 2x2 matrices:

A = [1 2]    B = [5 6] [3 4]        [7 8] AB = [1*5 + 2*7  1*6 + 2*8] [3*5 + 4*7  3*6 + 4*8] AB = [19 22] [43 50]

Common Applications

• Computer Graphics: Transformations and rotations
• Physics: Quantum mechanics and relativity
• Data Analysis: Principal Component Analysis (PCA)
• Machine Learning: Neural networks and linear regression
• Engineering: Structural analysis and circuit theory