Matrix Calculator
Perform comprehensive matrix operations including addition, multiplication, determinant, inverse, and more
Matrix Operations Calculator
Matrix A
Matrix B
Result:
Quick Examples:
Understanding Matrix Operations
Basic Operations
- Addition/Subtraction: Performed element-wise on matrices of same size
- Multiplication: Row-by-column multiplication (A×B requires columns of A = rows of B)
- Transpose: Flips matrix over its diagonal (rows become columns)
- Determinant: Scalar value that provides important matrix properties
Advanced Operations
- Inverse: Matrix A⁻¹ such that A × A⁻¹ = I (identity matrix)
- Rank: Maximum number of linearly independent rows or columns
- Eigenvalues: Special scalars associated with linear transformations
- Applications: Used in physics, computer graphics, and data analysis
Real-World Applications
Computer Graphics
3D transformations, rotations, scaling, and perspective projections in gaming and animation.
Engineering
Structural analysis, circuit analysis, control systems, and signal processing applications.
Data Science
Machine learning algorithms, principal component analysis, and statistical modeling.