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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transposed_matrix&oldid=15848
Transposed matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transposed_matrix&oldid=15848
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article