Given a matrix $A$, let us assume there is a equation: $Ax = b$
To solve for $x$, we can write:
$x = A^{-1} b$
One way to obtain the inverse of A is by single value decomposition:
Decomposition of $A$: $US(V^T)$, where $S$ is a diagonal matrix of singular values.
Therefore:
$Ax=b$
$US(V^T)x=b$
$x=(VW(U^T))b$, where $W=1/S$ along the diagonals.
Is there any other way instead of SVD to find the transpose of $A$.