Inorder to perform eigen decomposition, I converted a rectangular matrix to square by multiplying with the transpose of the matrix.
After decomposition, I got the component matrices. If I multiply the component matrices I would get the square matrix.
I would like to know, if there is any method for reconstructing the original rectangular matrix from the square matrix.
Thanks in advance
Best Answer
You are basically delving into singular value decomposition (SVD). Let $A$ be your rectangular matrix which of size $m\times n$. Let us assume $m<n$ (other way around is also same). Take $B_1=AA^T$ and $B_2=A^TA$. Take eigen decomposition of both. So that, $B_1=U\Lambda_1U^T$ and $B_2=V\Lambda_2V^T$. Now do the following