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Discussion on "Singular Value Decomposition: From the Math to C++ with Eigen" | Hashnode

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AbulAsar S.

Elixir |> JS/TS |> C++ |> AI enthusiast

Sep 30

Singular Value Decomposition: From the Math to C++ with Eigen

Introduction Imagine a cinema recording how many tickets it sells for each film every day. The rows of its table are days, the columns are films, and each number is a ticket count. Suppose Film A sell

abulasar.com15 min read

#svd #linear-algebra #cpp #eigen #mathematics #machine-learning

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Kartik N V J K

AI Developer | Making AI reliable, trustworthy & accessible to everyone | Active community contributor

The ticket-sales matrix is a clean way into this. One thing I would flag for anyone taking it to larger matrices: forming AᵀA explicitly squares the condition number, so for anything ill-conditioned, running Eigen's JacobiSVD or BDCSVD on A directly is more numerically stable than going through the eigen-decomposition of AᵀA. Did you stay with the AᵀA route mainly for the clarity of the derivation?

Oct 1

AbulAsar S.

Elixir |> JS/TS |> C++ |> AI enthusiast

Oct 1

Yes, exactly. I used the AᵀA route mainly to make the mathematical derivation easier to understand and connect SVD with eigenvalues and eigenvectors. For practical applications, I would use Eigen’s JacobiSVD or BDCSVD directly on A. Thanks for highlighting it!