I wanted to understand Singular Value Decomposition (SVD) hence consulted a few resources. In general I came across 2 different forms of SVD and hence got confused as to which one is correct or whether both are equivalent etc.
The 2 forms I came across are :
- Page 45 of deep learning book (http://www.deeplearningbook.org/contents/linear_algebra.html)
The singular value decomposition is similar, except this time we will write A as a product of three matrices: A = UDV^T$A = UDV^T$ (^T$^T$ implying transpose) Suppose that A$A$ is an m×n$m \times n$ matrix. Then U$U$ is defined to be an m×m$m \times m$ matrix, D$D$ to be an m×n$m \times n$ matrix, and V$V$ to be an n×n$n \times n$ matrix.
and
- Lec 47 of Mining Massive Datasets course (https://www.youtube.com/watch?v=P5mlg91as1c&list=PLLssT5z_DsK9JDLcT8T62VtzwyW9LNepV&index=47)
A = UDV^T$A = UDV^T$ (^T$^T$ implying transpose) Suppose that A$A$ is an m×n$m \times n$ matrix. Then U$U$ is defined to be an m×r$m \times r$ matrix, D$D$ to be an r×r$r \times r$ matrix, and V$V$ to be an n×r$n \times r$ matrix.
I consulted some more resources, it turns out that both the formulas are present in them as well. I need help to understand where is the gap in my understanding and what more do I need to cover (from a theoretical viewpoint) to bridge it.
