By Kardi Teknomo, PhD .
LinearAlgebra

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Transpose of a matrix is formed by interchanging the rows and columns of the input matrix.
If the input matrix size is m by n, the transpose matrix size is n by m.


Example:
Matrix Transpose Matrix Transpose


The notation of matrix transpose varies in the literatures, but in general we have three most used notation of matrix transpose: Matrix Transpose or Matrix Transpose , or Matrix Transpose . In this linear algebra tutorial, I adopt the first notation because it's clearer in the eyes.

The interactive program below produces matrix transpose of the input matrix. Random Example button provide you will unlimited examples of random matrix. Play with the two buttons or type your own input matrix to gain more understanding about matrix transpose.


Properties

Some important properties of matrix transpose are

  • Transpose of a (column) vector is a row vector and vice versa
  • The transpose of a transposed matrix returns the original matrix, Matrix Transpose
  • Transpose of the summation of two matrices is equal to the summation of their transposes Matrix Transpose
  • Transpose of the product of two matrices is equal to the product of their transposes taken in the reverse order, Matrix Transpose
  • The transpose of the matrix products can be extended to several matrices Matrix Transpose
  • The inverse of a transpose matrix is equal to the transpose of its inverse, Matrix Transpose

See also : matrix addition , matrix multiplication

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