Instead of Gaussian elimination, the crucialalgorithm becomes the singular value decomposition. Ratherthan concentrate on the basis transformation represented by linear system solution,the focus shiſts to maximal information compression. Linear algebra becomes the study of the basic operation of linear combination and its potential as a descriptor of large data sets. The focus naturally shiſts to the essential problem of efficient description of largedata sets using a small, typically incomplete set of feature vectors. The emphasis in linear algebra presentation suggested by data science is quite different.
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Neither is the essence of solving a linear system presented as the information-conserving coordinate transformation that it actually represents when the system matrix is of full rank. Such an approach is ill-suitedfor data science in which the primary interest is in efficient description of large data sets, and automated extraction of regularity from the available data. Presentation of the topic oſten links solutionsof linear sys- tems to posible intersections of lines or planes. Traditional presentations of linear algebra reflect its historical roots with a focus on linear systems and determinants, typically of small size. The theoretical foundations of the emerging discipline of Data Science are still being defined at present, but linear algebra is certainly one the cornerstones. Linear algebra for data science SORINMITRAN Department of Mathematics University of North Carolina at Chapel HillĪBSTRACT This textbook presents the essential concepts from linear algebra of direct utilityto analysis of large data sets.
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