# Transposed matrix

From Encyclopedia of Mathematics

The matrix obtained from a given (rectangular or square) matrix (; ) by interchanging the rows and the columns, that is, the matrix , where (; ). The number of rows of the transposed matrix is equal to the number of columns of , while the number of columns is equal to the number of rows of . The transpose of a matrix is usually denoted by or .

#### Comments

Some elementary properties of the transposition of matrices are , , , .

#### References

[a1] | F.R. [F.R. Gantmakher] Gantmacher, "The theory of matrices" , 1 , Chelsea, reprint (1959) pp. 19 (Translated from Russian) |

**How to Cite This Entry:**

Transposed matrix. O.A. Ivanova (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Transposed_matrix&oldid=15848

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098