Matrix Methods in Data Analysis by Bueno Cachadina, Maria Isabel; Perez Alvaro, Javier;

Hosszú leírás:

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This textbook offers a fresh and balanced approach to the study of Linear Algebra in the context of modern Data Science. Whereas many existing texts either emphasize theory with little connection to practice or jump straight to applications with minimal mathematical explanation, this book provides equal weight to both foundations and applications.

Designed for undergraduates who have completed a proof-based Linear Algebra course, it introduces concepts and tools from Matrix Analysis that are essential for Data Science and Machine Learning. Topics include:

• Vector norms and distances, orthogonality, and projections
• Matrix factorizations such as LU, CR, QR, and SVD
• Special matrix types: symmetric, positive definite, nonnegative, stochastic, and covariance matrices
• Key numerical algorithms, including the QR algorithm and the Power Method

Each chapter is enriched with real-world applications—from Google PageRank and Principal Component Analysis to clustering, dimensionality reduction, and linear regression—highlighting the role of matrix methods in Data Science.

To further support hands-on learning, the book is accompanied by a GitHub repository with Python labs, allowing students to implement the techniques covered and bridge the gap between theory and computation.

With its clear explanations, practical insights, and balance of theory and application, Matrix Methods in Data Analysis is an invaluable resource for courses in applied Linear Algebra, Data Science, and introductory Machine Learning.

Tartalomjegyzék:

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Part I: Linear Algebra And Machine Learning.- Why Should We Care?.- What You May Have Learned Before..- Core Topics.- Supplementary Topics.- Part II: Matrix Multiplication And Partitioned Matrices.- Why Should We Care?.- What You May Have Learned Before.- Core Topics.- Supplementary Topics.- From The Classroom To Real Life.- Part III: Norms, Distances, And Similarities.- Why Should We Care?.- What You May Have Learned Before.- Core Topics.- Supplementary Topics.- From The Classroom To Real Life.- Part IV: The Four Fundamental Subspaces Of A Matrix, And Gram-Matrices.- Why Should We Care? .- What You May Have Learned Before.- Core Topics.- Supplementary Topics.- From The Classroom To Real Life.- Part V: The Lu Factorization Of A Matrix.- Why Should We Care? .- What You May Have Learned Before.- Core Topics.- Supplementary Topics.- From The Classroom To Real Life.- Part VI: Orthogonality And The Qr Factorization.- Why Should We Care? .- What You May Have Learned Before.- Core Topics.- Supplementary Topics.- From The Classroom To Real Life.- Part VII: Orthogonal Projections And The Least Squares Problem.- Why Should We Care? .- What You May Have Learned Before.- Core Topics.- Supplementary Topics.- From The Classroom To Real Life.- Part VIII: Eigenvalues, Eigenvectors, And Algorithms.- Why Should We Care? .- What You May Have Learned Before.- Core Topics.- Supplementary Topics.- From The Classroom To Real Life.- Part IX: Symmetric And Positive Definite Matrices.- Why Should We Care? .- What You May Have Learned Before.- Core Topics.- Supplementary Topics.- From The Classroom To Real Life.- Part X: Singular Value Decomposition.- Why Should We Care? .- What You May Have Learned Before.- Core Topics.- Supplementary Topics.-From The Classroom To Real Life.- Part XI: Nonnegative Matrices And Perron Theory.- Why Should We Care? .- What You May Have Learned Before.- Core Topics.- Supplementary Topics.- From The Classroom To Real Life.- Index.