Matrix Methods in Data Analysis by Maria Isabel Bueno Cachadina and Javier Perez Alvaro is a 2026 textbook that develops linear algebra and matrix analysis specifically through the lens of modern data science and machine learning. Rather than treating linear algebra purely theoretically or jumping directly to applications, the book deliberately balances mathematical foundations with practical examples. It covers vector norms and distances, orthogonality and projections, matrix multiplication, the fundamental subspaces, Gram matrices, LU/CR/QR/SVD factorizations, and important classes of matrices such as symmetric, positive-definite, stochastic, covariance, and nonnegative matrices.
A major strength of the book is its emphasis on showing why matrix methods matter in real data analysis. Mathematical concepts are connected to applications such as Google PageRank, Principal Component Analysis (PCA), clustering, dimensionality reduction, and linear regression, while numerical methods such as the Power Method and QR algorithm demonstrate how these ideas are implemented computationally.
The 1,004-page book is aimed primarily at undergraduates who already have a proof-based linear algebra background and is supplemented by Python laboratories hosted through GitHub, making it a bridge between traditional mathematics, numerical linear algebra, and practical machine learning.
BOOK
A major strength of the book is its emphasis on showing why matrix methods matter in real data analysis. Mathematical concepts are connected to applications such as Google PageRank, Principal Component Analysis (PCA), clustering, dimensionality reduction, and linear regression, while numerical methods such as the Power Method and QR algorithm demonstrate how these ideas are implemented computationally.
The 1,004-page book is aimed primarily at undergraduates who already have a proof-based linear algebra background and is supplemented by Python laboratories hosted through GitHub, making it a bridge between traditional mathematics, numerical linear algebra, and practical machine learning.
BOOK
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