How deeply does Grokking Machine Learning cover singular value decomposition?

Explains the smaller-matrix idea and names an application, but gives no decomposition procedure.

Singular value decomposition

As explained in Grokking Machine Learning

A matrix decomposition that expresses a matrix as the product of orthogonal matrices and a diagonal matrix of singular values.

Singular value decomposition is a way to simplify a large data matrix by expressing it as a product of smaller matrices, reducing both its rows and columns. section 2.3 section 2.5

Clustering can reduce a dataset’s rows, while dimensionality reduction can reduce its columns; SVD is presented as a way to simplify both at once. section 2.3 section 2.5

Image compression

Treat a black-and-white image as a table whose entries are pixel intensities. Singular value decomposition is used in image compression. section 2.3

How Grokking Machine Learning covers it

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Also explained in

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Data Without LabelsSingular value decomposition is a matrix factorization that expresses a matrix as the product of two orthogonal matrices and a diagonal matrix of singular values.
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Math and Architectures of Deep LearningThe statement that any matrix can be decomposed as a product of orthogonal matrices and a diagonal matrix in singular value decomposition form.
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LLMs in ProductionSingular value decomposition is a matrix factorization that expresses a matrix as a product of orthogonal and diagonal matrices.
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Natural Language Processing in Action, Second EditionSingular value decomposition is a matrix factorization that expresses a matrix as the product of orthogonal singular-vector matrices and a diagonal singular-value matrix.
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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIA matrix factorization that expresses a matrix as the product of orthogonal matrices and a diagonal matrix of singular values.

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Related concepts

principal component analysisused by · Principal component analysis is a linear dimensionality-reduction technique that transforms data into orthogonal components ordered by the variance they capture.
singular valueproduces · A singular value is a nonnegative scalar in a matrix’s singular value decomposition that measures stretching along a corresponding singular direction.
co-occurrence matrixuses · A co-occurrence matrix is a table whose entries record the frequency or weight with which pairs of items occur together within specified contexts.
dimensionality reductionuses · Dimensionality reduction is the transformation of data into a representation with fewer dimensions while retaining selected information, structure, or relationships.
truncated singular value decompositionincludes · Truncated singular value decomposition is a matrix factorization technique that approximates a matrix using a selected number of singular components.
compressionuses · Compression is the transformation of information into a more compact representation to reduce storage or transmission requirements while retaining information needed for recovery or use.

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