Math and science::Algebra

Transpose characterized

Instead of thinking of the matrix transpose as the swapping of rows and columns, there is a more meaningful characterization:

Matrix transpose

Let $A$ be an $m \times n$ matrix and $x \in R^{n}$ and $y \in R^{m}$ be column vectors. Then the transpose of $A$ , denoted $A^{T}$ is the matrix such that the following holds:

[

? = ?

]

16.10.2024