# Doubt about transpose operation in SVD matrix tutorial

I am trying to get a grasp of the Singular value Decomposition of a matrix following this tutorial.

I am confused however by the way they transpose the matrix A. From what I understood from the transposition operation,
|A |B | ----------------------------- |A |C |0 |0 |
|C |D | --- should transpose to --- |B |D |0 |0 |
|0 |0 |
|0 |0 |

Or did I misunderstand the transpose process?

• Are you asking what a matrix transpose is? Or something else?
– Sycorax
Commented May 28, 2021 at 3:53

Your understanding is correct; that's how transposes work.

I think you're asking because the page shows the computation of $$A A^T = W$$, but the transpose $$A^T$$ is incorrect. Their given value of $$W$$ is correct according to the conventional definition of transpose (which you gave), so it seems that it's only $$A^T$$ that's incorrectly written.

Given that $$$$A = \begin{bmatrix} 2 & 4 \\ 1 & 3 \\ 0 & 0 \\ 0 & 0 \end{bmatrix}$$$$ the transpose should be $$$$A^T = \begin{bmatrix} 2 & 1 & 0 & 0 \\ 4 & 3 & 0 & 0 \end{bmatrix}$$$$ and not $$$$A^T \color{red}{\neq} \begin{bmatrix} 2 & \color{red}{4} & 0 & 0 \\ \color{red}{1} & 3 & 0 & 0 \end{bmatrix}$$$$ which your linked tutorial gave.

It might be nice to email the owner of the page to clue them in. :)

• Thats what I thought but as I did not really get the SVD, I was wondering if i misundertood everything, thanks. that means the whole calculations are false right? Commented May 28, 2021 at 4:24
• They only wrote $A^T$ down wrong; they didn't use it incorrectly in their calculations. $W$ is correct, and I assume everything following it is too, but I'm not going to check the entire page. Commented May 28, 2021 at 4:28
• alright if W is correct then it should be fine, thanks Commented May 28, 2021 at 4:29