Matrix Transpose Calculator

Swap rows ↔ columns

CalculatorsFreeNo Signup
4.4(821 reviews)
All Tools

Loading tool...

About Matrix Transpose Calculator

A matrix transpose calculator that swaps rows and columns of any m×n matrix. Checks if the matrix is symmetric (A = Aᵀ) or skew-symmetric (A = −Aᵀ), shows dimensions before/after, and verifies transpose properties like (AB)ᵀ = BᵀAᵀ. Supports up to 6×6 matrices. All calculations are client-side.

Matrix Transpose Calculator Features

  • Transpose
  • Symmetric check
  • Dim display
  • Up to 6×6
  • Properties
The transpose of matrix A (written Aᵀ) is formed by turning rows into columns. If A is m×n, then Aᵀ is n×m. Key properties: (Aᵀ)ᵀ = A, (A+B)ᵀ = Aᵀ+Bᵀ, (cA)ᵀ = cAᵀ, (AB)ᵀ = BᵀAᵀ. A matrix is symmetric if A = Aᵀ.

How to Use

Enter your matrix:

  • Size: Set rows and columns
  • Values: Fill in entries
  • Result: Transposed matrix shown

Symmetric Matrices

  • A = Aᵀ: symmetric
  • A = −Aᵀ: skew-symmetric
  • Symmetric matrices have real eigenvalues

Applications

Transpose is used in least squares regression (AᵀA), covariance matrices, graph theory (adjacency matrices), and quantum mechanics.

Step-by-Step Instructions

  1. 1Set matrix dimensions.
  2. 2Enter matrix values.
  3. 3View the transpose.
  4. 4Check symmetric/skew.
  5. 5Compare dimensions.

Matrix Transpose Calculator — Frequently Asked Questions

What happens to dimensions when transposing?+

A 3×4 matrix becomes 4×3. The entry at position (i,j) moves to (j,i). Square matrices stay the same size.

What is a symmetric matrix?+

A square matrix where A = Aᵀ, meaning aᵢⱼ = aⱼᵢ. The matrix is mirrored along its main diagonal. All eigenvalues of a real symmetric matrix are real.

Why does (AB)ᵀ = BᵀAᵀ and not AᵀBᵀ?+

The order reverses because matrix multiplication is not commutative. Think of it like reversing socks and shoes: to undo (socks then shoes), you remove shoes first, then socks.

More Calculators Tools

Explore all 639 other calculators tools available on Generatr

1-Sample Z-Test Calculator2-Sample Z-Test Calculator3D Surface Area CalculatorA/B Testing Significance CalculatorAbsolute Value CalculatorAbundant Number CheckerAccelerated Aging CalculatorAchromatic Number CalculatorAcyclic Chromatic Number CalculatorAdditive Persistence CalculatorAge CalculatorAging Test CalculatorAlbertson Index CalculatorAlgebraic Connectivity CalculatorAliquot Sequence CalculatorAliquot Sum CalculatorAlternating Series Test CalculatorAmicable Number FinderAnnuity CalculatorAPY CalculatorAquarium CO2 Drop CheckerArea CalculatorArea Under Curve CalculatorArithmetic Sequence CalculatorArmstrong Number CalculatorASCVD Risk CalculatorAspect Ratio CalculatorAtom Bond Connectivity CalculatorAugmented Eccentric Connectivity CalculatorAugmented Zagreb Index Calculator
View all 639 calculators tools
Share this tool: