09-23-2026, 04:41 PM
Christoph Börgers’ Introduction to Numerical Linear Algebra is a textbook designed to introduce students to the computational side of linear algebra: how mathematical matrix problems are actually solved on computers. It assumes some prior linear algebra but reviews essential concepts as needed.
The book begins with Gaussian elimination, LU/PLU decompositions, band matrices, computational cost, vector and matrix norms, conditioning, and the distinction between ill-conditioned problems and unstable algorithms. A recurring theme is that numerical computation is not simply about obtaining an answer, but about understanding how accurate and reliable that answer can be when calculations involve finite precision.
The later chapters develop more sophisticated techniques for nonsquare systems, orthogonal and symmetric matrices, QR decomposition, eigenvalue computation, power iteration, and the singular value decomposition (SVD). What makes the book distinctive is its emphasis on applications: diffusion problems, computed tomography, GPS, stability of equilibria, multigrid methods, and even applications of the SVD to grading.
The author also develops the QR eigenvalue method from power iteration rather than presenting it as a black box. Overall, it is intended as a one-semester undergraduate or beginning-graduate course and connects theoretical linear algebra with scientific computing and data science.
BOOK
The book begins with Gaussian elimination, LU/PLU decompositions, band matrices, computational cost, vector and matrix norms, conditioning, and the distinction between ill-conditioned problems and unstable algorithms. A recurring theme is that numerical computation is not simply about obtaining an answer, but about understanding how accurate and reliable that answer can be when calculations involve finite precision.
The later chapters develop more sophisticated techniques for nonsquare systems, orthogonal and symmetric matrices, QR decomposition, eigenvalue computation, power iteration, and the singular value decomposition (SVD). What makes the book distinctive is its emphasis on applications: diffusion problems, computed tomography, GPS, stability of equilibria, multigrid methods, and even applications of the SVD to grading.
The author also develops the QR eigenvalue method from power iteration rather than presenting it as a black box. Overall, it is intended as a one-semester undergraduate or beginning-graduate course and connects theoretical linear algebra with scientific computing and data science.
BOOK
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