Find the Transpose of a Matrix

The transpose is the quiet workhorse of linear algebra — swap rows and columns, and matrices rotate, normalise, and slot into formulas they had no business fitting before. It is the operation behind inner products, statistical data layouts and most neural network notation, and it is trivial to define but tedious to apply by hand the moment the matrix grows.

Find the Transpose of a Matrix does the swap instantly and exactly. Paste or type any matrix — rows on lines, separated by spaces or commas, in plain or bracket notation — and the result comes back with rows and columns exchanged, both dimensions printed, and the output aligned column by column for reading and pasting. Decimals, negatives and fractions all work, and nothing ever leaves your browser.

• Instant row–column swap: The transpose is computed the moment you paste.
• Flexible input: Rows on lines, space or comma separated, or full bracket notation — all detected automatically.
• Rectangular matrices supported: An m×n matrix correctly becomes n×m, with both dimensions shown.
• Decimals, negatives and fractions: Any number format you paste is preserved exactly.
• Aligned output: Columns are right-aligned so the result reads like a textbook matrix.
• Dimensions reported: Original and transposed sizes are printed with the result.
• Copy or download: Ready for notes, spreadsheets and code.
• Free and private: All computation happens in your browser; nothing is uploaded.

1. Enter the matrix. Type or paste each row on its own line — "1 2 3" then "4 5 6" — or use the bracket form [[1,2,3],[4,5,6]].
2. Check the preview. The tool reads the matrix live; a summary line shows the dimensions it detected.
3. Read the transpose. Rows and columns are swapped and the result is aligned automatically.
4. Verify the dimensions. The output notes that an m×n matrix became n×m.
5. Copy or download. Take the result to your document, spreadsheet or code.
6. Retry with different input. Editing any entry updates the transpose immediately.

Example 1 — Classroom exercise. Given the matrix with rows "1 2 3" and "4 5 6", the tool returns the transpose with rows "1 4" and "2 5" and "3 6" — the 2×3 matrix becoming 3×2, exactly as the textbook answer.

Example 2 — Data layout. A statistics sheet where each row is a sample and each column a variable can be flipped so variables become rows. Paste the table, get the transpose, paste it back into the spreadsheet.

Example 3 — Symmetry check. Paste a symmetric matrix like "1 2 3 / 2 4 5 / 3 5 6". The transpose returns the identical matrix — an instant visual proof of symmetry.

Example 4 — Product rule practice. Verifying (AB)ᵀ = BᵀAᵀ? Transpose two small matrices with this tool and check the rule by hand — each side computed in seconds.

• Instant results: No row-by-row copying by hand, no off-by-one errors.
• Any shape: Square or rectangular, large or small, exact every time.
• Input flexibility: Accepts the formats people actually paste.
• Teaching value: Dimensions shown explicitly make the operation click for students.
• Clean output: Aligned columns that paste into documents and spreadsheets unchanged.
• Free and private: Runs entirely in the browser; nothing is uploaded.