Linear Algebra

Singular Value Decomposition (SVD)

First heard from f1tenth.

Resources

• Singular Value Decomposition playlist by Steve Brunton

Also mentioned from this video https://www.youtube.com/watch?v=jBnCcr-3bXc 10:30 for Zero-shot Learning.

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any $m\times n$ matrix.

Be familiar with your eigenvalues

This is a prerequisite. I still forget the point of eigenvalues.

Resources:

• https://www.youtube.com/watch?v=mBcLRGuAFUk&ab_channel=MITOpenCourseWare
• 5 minute explanation https://www.youtube.com/watch?v=giOpcCPHitY&ab_channel=CyrillStachniss by Cyrill Stachniss

$A=U\Sigma V^T$

• $U$ is $m\times m$, and a Orthogonal Matrix
• $\Sigma$ is $m\times n$, and a Diagonal Matrix
• $V$ is $n\times n$, and an Orthogonal Matrix as well

Look at $A^{T}A$

Singular value

Related

• Polar Decomposition