#algebra 

The **transpose** of a [[Matrix|matrix]] is an operator that flips a matrix over its main diagonal, that is, it switches the row and column indices of the matrix $\LARGE A$ by producing another matrix, denoted by $\LARGE A^T$.

На русском языке называется **транспонированная матрица**.

![[Pasted image 20241003204503.png]]

![[Pasted image 20241124190701.png]]
## Свойства
$$\LARGE (A^T)^T=A$$
$$\LARGE (A+B)^T=A^T+B^T$$
$$\LARGE (AB)^T=B^TA^T$$$$\LARGE (cA)^T=cA^T$$
$$\LARGE \det{A}=\det{A^T}$$
where $\LARGE \det$ is the [[Determinant of a matrix]].

Докажем свойство 3:
![[Pasted image 20241124190631.png]]