Transposed matrix

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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 .


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


[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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098