Matrix Calculator
Perform matrix operations: addition, multiplication, determinant, inverse, transpose, and more
Matrix Operations
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
What Operations Can You Perform with This Matrix Calculator?
This free Matrix Calculator handles the core operations of linear algebra in one place: addition, subtraction, multiplication, transpose, determinant, and inverse. Enter your matrix values, select the dimensions and operation, and get an accurate result instantly. Matrix addition and subtraction require both matrices to share the same dimensions, while multiplication requires the column count of the first matrix to match the row count of the second. The inverse only exists for square matrices with a non-zero determinant. This tool is built for students working through linear algebra coursework, engineers solving systems of equations, and developers handling data transformations or 3D graphics. No manual arithmetic, no errors from carrying numbers by hand.