Quadratic Equation Solver (ax² + bx + c = 0)
About Matrix Multiplication Calculator
The Matrix Multiplication ($A \times B$) & Dot Product Calculator performs algebraic matrix multiplication for $m\times k$ and $k\times n$ matrices with step-by-step row-column dot product breakdowns, powers ($A^n$), and LaTeX export.
How to Use Matrix Multiplication Calculator
Step 1
Set dimensions for Matrix A ($m\times k$) and Matrix B ($k\times n$).
Step 2
Enter numbers into both matrix grids.
Step 3
Click "Multiply Matrices (A × B)".
Step 4
Inspect the step-by-step row-by-column dot product breakdown.
Practical Use Cases for Matrix Multiplication Calculator
3D Graphics Affine Transformations & Camera Projections
Multiply sequence of $4\times4$ translation, rotation, and scaling matrices to compute composite model-view-projection (MVP) transforms.
Neural Network Forward Propagation & Linear Layers
Calculate tensor dot products ($Y = XW + b$) between weight matrices and input activation vectors.
Input & Output Examples
Multiplying 2x3 Matrix by 3x2 Matrix
A (2x3): `[[1, 2, 3], [4, 5, 6]]`, B (3x2): `[[7, 8], [9, 1], [2, 3]]`
Result C (2x2): `[[31, 19], [85, 55]]` | Element C₁₁ = (1×7)+(2×9)+(3×2) = 31
Key Features & Performance
- ✓Multiplies any conformable matrix dimensions ($m\times k$ by $k\times n = m\times n$).
- ✓Interactive Step-by-Step Dot Product Explorer: highlight any cell in result matrix $C$ to see exact row $A_i$ and column $B_j$ dot product math.
- ✓Matrix Powers: computes $A^2, A^3, A^n$ using fast binary matrix exponentiation.
- ✓100% Client-Side linear algebra engine.
- ✓1-Click Copy result matrix in LaTeX, Python NumPy, and MATLAB.
Key Terminology & Definitions
Matrix Multiplication Rule
The product $AB$ exists if and only if the number of columns in $A$ equals the number of rows in $B$. Entry $c_{ij} = \sum_{k} a_{ik} b_{kj}$.
Non-Commutative Property
In linear algebra, matrix multiplication is generally not commutative ($AB \neq BA$).