Matrix Transpose Calculator

Calculate the transpose of a matrix. Free online matrix transpose calculator.

The Matrix Transpose Calculator swaps rows and columns of any matrix, creating the transpose Aᵀ. The element at position (i,j) moves to position (j,i). Enter your matrix to find its transpose instantly. This fundamental operation is essential for matrix algebra, data manipulation, and many applications in science and engineering.

Common use cases

  • Matrix algebra operations
  • Data reshaping
  • Symmetric matrix checking
  • Least squares solutions
  • Covariance matrices

How to use

  1. Enter your matrix dimensions
  2. Input the matrix elements
  3. Click transpose to calculate
  4. View the resulting matrix
  5. Compare original and transpose

FAQ

What is a transpose?

The transpose flips a matrix over its diagonal: rows become columns and vice versa. (Aᵀ)ᵢⱼ = Aⱼᵢ.

What dimensions does the transpose have?

An m×n matrix becomes n×m. A 3×2 matrix transposes to a 2×3 matrix.

What is a symmetric matrix?

A matrix where A = Aᵀ. These arise naturally in many applications.

What are properties of transpose?

(Aᵀ)ᵀ = A, (A+B)ᵀ = Aᵀ+Bᵀ, (AB)ᵀ = BᵀAᵀ, and (cA)ᵀ = cAᵀ.