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Transpose of a Matrix

Tool to compute the transpose of a matrix. The transpose of a matrix M of size mxn is a matrix denoted tM of size nxm created by swapping lines and columns.

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Transpose of a Matrix -

Tag(s) : Mathematics,Algebra,Symbolic Computation

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Transpose of a Matrix

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Also on dCode: Inverse of a Matrix

Tool to compute the transpose of a matrix. The transpose of a matrix M of size mxn is a matrix denoted tM of size nxm created by swapping lines and columns.

Answers to Questions

How to calculate the transpose of a matrix?

The transposition of a matrix is one of the simplest matrix operations to perform. On has to invert lines and columns:$$ \text{ If } M = \begin{pmatrix} a & c & e \\ b & d & f \end{pmatrix} \text{ Then } M^T = \begin{pmatrix} a & b \\ c & d \\ e & f \end{pmatrix} $$

The transposition is valid on both square matrices and rectangular matrices. A transposed row vector is a column vector.

The transposition operation is noted with a T or t (uppercasehref or lowercasehref).

What is a double transposition?

Transposing twice a matrix returns it unchanged.

The double transpositionhref is the name given to a cryptographic cipher.

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