Matrix Calculator
Perform matrix operations: addition, multiplication, determinant, inverse, transpose, and more
Matrix Operations
Matrix A
Matrix B
Matrix
Matrix (must be square and det ≠ 0)
Matrix
Matrix (square matrix only)
Result
What is a Matrix?
A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are fundamental tools in linear algebra with applications across science, engineering, computer graphics, and data science.
Matrix Operations Explained
- Addition/Subtraction: Add or subtract corresponding elements (matrices must be same size)
- Multiplication: Row-by-column dot product (columns of A must equal rows of B)
- Determinant: A scalar value that determines if a matrix is invertible (det ≠ 0)
- Inverse: A matrix that when multiplied by the original yields the identity matrix
- Transpose: Flips rows and columns (Aij becomes Aji)
- Scalar Multiplication: Multiply every element by a constant value
Real-World Applications
- Computer Graphics: 3D transformations, rotations, and scaling in games and animation
- Machine Learning: Neural network weights, data representation, and feature matrices
- Engineering: Structural analysis, electrical circuit analysis, and robotics
- Economics: Input-output models and optimization problems
- Physics: Quantum mechanics, relativity, and rigid body dynamics
- Image Processing: Filters, convolutions, and transformations