Matrix Multiplication Calculator
Multiply two matrices and compute the resulting matrix and operation count.
Inputs
Result Elements
6
Total Scalar Operations
42
Multiplications
24
Step by step
Result matrix shape
(3×4) × (4×2)
= 3×2
Scalar multiplications: m × k × n
3 × 4 × 2
= 24
Scalar additions: m × (k−1) × n
3 × 3 × 2
= 18
How it works
Matrix multiplication (matmul) is the core operation in neural networks — every linear layer, attention mechanism, and convolution can be expressed as matmuls. For A(m×k) × B(k×n), the result is an m×n matrix requiring m×k×n multiplications and m×(k-1)×n additions.
Formula
Matrix Multiply
C[i,j] = sum(A[i,k] * B[k,j]) for k=1..K
- m, k, n
- Dimensions of input and output matrices
Frequently Asked Questions
Why is matrix multiplication so important in deep learning?
Every fully connected layer computes Y = XW + b, which is a matrix multiplication. Transformers, CNNs (via im2col), and RNNs all reduce to batched matmuls, making it the single most performance-critical operation in ML.
How does this relate to FLOPs calculations?
The FLOPs for a matmul are typically counted as 2×m×k×n (counting multiply and add as separate operations), which is the standard used by hardware vendors and ML papers.