How does the Matrix Transpose work?

(Aᵀ)ᵢⱼ = Aⱼᵢ Then: Rows become columns Then: (Aᵀ)ᵀ = A Then: (AB)ᵀ = BᵀAᵀ.

Can you give an example of how to use the Matrix Transpose?

Example: Input [[1,2,3],[4,5,6]] gives a result of [[1,4],[2,5],[3,6]].

Is the Matrix Transpose free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Matrix Transpose?

Our Matrix Transpose uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Matrix Transpose

Matrix (one row per line)

The transpose of a matrix swaps its rows and columns. If A is an m×n matrix, Aᵀ is an n×m matrix. Transposes are used in linear algebra, machine learning, and solving systems of equations.

Symbol	Name	Unit	Description
A	original matrix	—	—
Aᵀ	transposed matrix	—	—

Property	Formula
Double transpose	(Aᵀ)ᵀ = A
Sum	(A+B)ᵀ = Aᵀ+Bᵀ
Product	(AB)ᵀ = BᵀAᵀ
Scalar	(cA)ᵀ = cAᵀ
Symmetric matrix	A = Aᵀ

References

›Matrix transpose — Khan Academy

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