Matrix Calculator
Perform 2×2 and 3×3 matrix operations: addition, subtraction, multiplication (A×B), transpose (Aᵀ), and determinant det(A). Essential for A-Level Further Maths, IB HL, and linear algebra.
Matrix A
Matrix B
| Curriculum | Matrix Coverage | Convention | Software |
|---|---|---|---|
| 🇬🇧 UK A-Level Further Maths | 2×2 and 3×3, det, inverse, transformations | Column vectors (standard in UK) | Casio ClassPad |
| 🌐 IB HL Mathematics | 2×2, det, inverse, systems of equations | Varies (mostly column vectors) | GDC (TI or Casio) |
| 🇺🇸 US Linear Algebra | Full matrix theory (university level) | Row vectors common in ML/CS | MATLAB, Python numpy |
| 🇩🇪 Germany Abitur | Lineare Algebra — up to 3×3 | Column vectors preferred | CASIO fx-CG or GeoGebra |
| 🇯🇵 Japan (数学C) | 2×2 matrices and linear transformations | Column vectors | Casio calculators |
| 💻 Machine Learning / CS | Arbitrary size; batched operations | Row vectors (convention) | numpy, PyTorch, TensorFlow |
Frequently Asked Questions
Why is row vector vs column vector convention different in the US vs Europe?
European mathematics textbooks (UK, Germany, France) traditionally write vectors as column vectors, which means transformations are applied as T×v (matrix times column vector on the right). In US computer science and machine learning contexts, row vectors are often used, meaning transformations are applied as v×T (row vector times matrix on the left). NumPy and most ML frameworks use row-vector convention by default (shape [n] is treated as a 1×n row vector). This causes confusion when switching between textbooks and code. Always check which convention your textbook or software uses.
Where are matrices used in real life?
Matrices are foundational across many fields: Computer graphics (3D rotation, scaling, and translation matrices power every video game and 3D animation). Machine learning (neural networks are essentially large matrix multiplications). Cryptography (Hill cipher uses matrix operations). Economics (input-output analysis, Leontief model). Quantum mechanics (state matrices / density matrices). Engineering (finite element analysis, structural calculations). Google's PageRank algorithm is a matrix operation. Every major country's engineering curriculum includes matrix algebra for these reasons.