Transpose of a matrix
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Revision 3919
9/5/2026, 4:05:29 PM · SalixBabylonica
Added exercise "Mes premières transposées de matrices"
linked exercisesNoneMes premières transposées de matrices
Revision 3365
9/1/2026, 8:22:34 AM · Ancient Tree
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##### Intuition2
The transpose of a [[Matrix|matrix]] is a new matrix obtained by interchanging the columns and rows of the initial matrix.2
The transpose of a [[Matrix|matrix]] is a new matrix obtained by interchanging the rows and columns of the initial matrix.3
4
For example,5
$$6
\begin{pmatrix}7
1 & 2 & 3\\8
4 & 5 & 69
\end{pmatrix}^{T}10
=11
\begin{pmatrix}12
1 & 4\\13
2 & 5\\14
3 & 615
\end{pmatrix}.16
$$17
4
##### Formal definition5
Let6
$$7
A=(a_{ij})_{1\le i\le m,\ 1\le j\le n}8
$$9
be an $m\times n$ matrix. The transpose of $A$, denoted by $A^T$, $A^t$, or ${}^tA$, is the $n\times m$ matrix10
$$11
A^T=(a_{ji})_{1\le i\le n,\ 1\le j\le m}.12
$$Revision 3364
9/1/2026, 8:21:17 AM · Ancient Tree
Updated text
Compare with revision 336311 changed lines
1
##### Intuition1
The transpose of a [[Matrix|matrix]] is a new matrix obtained by interchanging the columns and rows of the initial matrix.2
3
Let $A = (a_{ij})_{m\le i \le n,k \le j \le l}$ be a matrix. The transpose of $A$, written $A^{T}$, $A^{t}$ or $^{t}A$ is equal to $(a_{ji})_{k \le j \le l, m\le i \le n}$.4
##### Formal definition5
Let6
$$7
A=(a_{ij})_{1\le i\le m,\ 1\le j\le n}8
$$9
be an $m\times n$ matrix. The transpose of $A$, denoted by $A^T$, $A^t$, or ${}^tA$, is the $n\times m$ matrix10
$$11
A^T=(a_{ji})_{1\le i\le n,\ 1\le j\le m}.12
$$Revision 3363
9/1/2026, 8:19:05 AM · araucaria araucana
Updated text
Compare with revision 2694 changed lines
1
The transpose of a [[Matrix|matrix]] is...1
The transpose of a [[Matrix|matrix]] is a new matrix obtained by interchanging the columns and rows of the initial matrix.2
3
Let $A = (a_{ij})_{m\le i \le n,k \le j \le l}$ be a matrix. The transpose of $A$, written $A^{T}$, $A^{t}$ or $^{t}A$ is equal to $(a_{ji})_{k \le j \le l, m\le i \le n}$.Revision 269
7/7/2026, 10:47:07 AM · Ancient Tree
Concept edited
Compare with revision 2682 changed lines
1
The transpose of a matrix is...1
The transpose of a [[Matrix|matrix]] is...Revision 268
7/7/2026, 10:46:58 AM · Ancient Tree
Concept created
The transpose of a matrix is...