What does transposing a matrix mean?

It means rewriting the matrix so its rows become columns and its columns become rows. The value at row i, column j in the original matrix moves to row j, column i in the transpose.

Does the matrix have to be square?

No, any matrix can be transposed. An M by N matrix becomes an N by M matrix after transposing, only square matrices keep the same dimensions.

Are decimal values supported?

Yes, each value is parsed as a floating-point number, so both whole numbers and decimals like 3.5 or -0.25 work.

What happens if my rows have different lengths?

The tool checks that every row has the same number of values and returns a clear error naming the mismatched row if one doesn't match, since a matrix requires consistent row lengths.

Matrix Transpose Calculator - Flip Rows and Columns Online

Overview

Introduction

Transposing a matrix, swapping its rows and columns, is one of the most basic operations in linear algebra, used constantly in everything from statistics to computer graphics.

This tool handles it for a matrix of any size, including non-square ones and matrices with decimal values.

What Is Transpose a Matrix?

The transpose of a matrix is a new matrix where the original's rows become columns (and vice versa). If the original is M rows by N columns, the transpose is N rows by M columns.

It's usually written with a superscript T, so the transpose of matrix A is written A^T.

How Transpose a Matrix Works

The input is split into rows on newlines and values on commas, with each value parsed as a floating-point number; blank lines are ignored and every row must have the same number of values.

The value originally at row i, column j is placed at row j, column i in the output, which is then formatted back into the site's standard matrix notation.

When To Use Transpose a Matrix

Use it whenever you need to reorient a matrix, for example to make a matrix multiplication's dimensions line up, or to convert a set of row vectors into column vectors.

It's also useful for double-checking a transpose you've computed by hand.

Often used alongside Find the Determinant of a Matrix, Generate an Identity Matrix and Generate Random Matrices.

Features

Advantages

Works on matrices of any dimensions, not just square ones.
Preserves decimal precision exactly since no arithmetic is performed, only repositioning.

Limitations

Every row in the input must have the same number of values, a ragged input is rejected with an error.

Examples

Transposing a 2x3 matrix

Input

1,2,3
4,5,6

Output

1,4
2,5
3,6

The 2 row by 3 column input becomes a 3 row by 2 column output; row 1 (1,2,3) becomes column 1 of the result.

Best Practices & Notes

Best Practices

Double-check the input has one row per line and consistent comma-separated values before submitting.

Developer Notes

transposeMatrix() builds the result with Array.from() over the column count for the outer loop and the row count for the inner loop, reading `matrix[row][col]` at position `[col][row]`, a direct index swap with no matrix arithmetic involved.

Transpose a Matrix Use Cases

Aligning matrix dimensions before a multiplication
Converting between row-vector and column-vector representations
Checking a hand-computed transpose for a linear algebra assignment

Common Mistakes

Assuming the transpose of a non-square matrix keeps the same dimensions, an M by N matrix becomes N by M, not M by N.
Leaving a row with a different number of values than the others, which the parser flags as an error rather than silently padding.

Tips

Transposing a matrix twice returns the original matrix, a quick way to sanity-check the tool.

Transpose a Matrix