How to decompose any matrix into rotation and stretch
In short: Discover the mechanics of Singular Value Decomposition, a fundamental process that breaks a matrix down into its core geometric components.
In this lecture from MIT's RES.18-009 course, instructors Gilbert Strang and Cleve Moler explain the SVD process. The decomposition factors a matrix into three distinct parts: an orthogonal matrix, a diagonal matrix containing the singular values, and a second orthogonal matrix. Geometrically, this represents a sequence of rotation, followed by stretching, and a final rotation.
Opens the Intellect+ feed with this card first. Swipe up for the next one.
Sources
- Summary by Intellect · source: Singular Value Decomposition (the SVD)
To cite this card, link to https://intellectplus.co.uk/app/ideas-singular-value-decomposition-the-svd.
How we source, check and correct cards: Editorial standards.
General information, not professional advice. Spotted an error? Flag the card or see corrections and complaints.
Intellect Plus is a visual educational discovery platform for exploring fascinating facts and ideas. Brain Food, Not Brain Rot. What is Intellect Plus?
Related
More in Mathematics · More in Ideas & Philosophy · Latest · A–Z · All topics
