Enter Matrices
Supports decimals and simple fractions like 3/4Results
Run a calculation to see the result and detailed steps.
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Example data table
Matrix A (2×3)
| 2 | 0 | 1 |
| -1 | 3 | 4 |
Matrix B (3×2)
| 1 | 5 |
| 2 | -1 |
| 0 | 3 |
Preset: Identity × Matrix (3×3)
Quick sanity check: I3 · M = M
Matrix A (I3)
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
Matrix B (3×3)
| 2 | -1 | 4 |
| 0.5 | 3 | 0 |
| 7 | 2 | -3 |
Preset: 2D Rotation 45° × Points (2×2 · 2×3)
Rotate 3 points by 45° using a standard rotation matrix.
Matrix A (Rotation 45°)
| 0.70710678 | -0.70710678 |
| 0.70710678 | 0.70710678 |
Matrix B (Points as columns)
| 1 | 0 | -1 |
| 0 | 1 | 2 |
Formula used
If A is m×n and B is n×p, the product C = AB is m×p with entries:
cij = Σnk=1 aik · bkj
Each result cell is a dot product between a row of A and a column of B.
How to use
- Choose dimensions so columns of A equal rows of B.
- Click “Build inputs” to refresh the entry grids.
- Enter numbers; decimals and simple fractions like 5/8 work.
- Set precision for rounding the displayed outputs.
- Press “Calculate” to see results and per-cell steps.
- Export the result table as CSV or PDF if needed.
How to calculate FLOPs for matrix multiplication
For A of size m×n and B of size n×p:
- Multiplications = m × n × p
- Additions = m × p × (n − 1)
- Exact FLOPs = mnp + mp(n − 1) = 2mnp − mp
- Approximate FLOPs (HPC convention) = 2mnp
Multiplications: —
Additions: —
Exact FLOPs: —
Approx. FLOPs (2mnp): —
Note: Some references count a fused multiply–add (FMA) as 2 FLOPs. The exact count above uses n−1 additions per dot product.
FAQs
You can choose from 1 to 8 for rows and columns. Ensure columns of A equal rows of B for the multiplication to be valid.
Both decimals and simple fractions like 3/4 are accepted. Scientific notation such as 1.2e3 also works.
Choose the “Precision” value to round displayed results. Internally, calculations use standard floating‑point arithmetic.
Yes. Buttons beside Matrix A and Matrix B export the current input grids as CSV files.
The page uses browser rendering to capture the results area and generate a PDF file for download.
Matrix multiplication requires that A’s columns equal B’s rows. Adjust sizes so they match this rule.
Yes. Use a square identity matrix (ones on the diagonal, zeros elsewhere) of compatible size to leave the other matrix unchanged.