Linear Algebra for Intelligent Systems: Vectors, Matrix Theory, Decompositions, Optimization, and Data Modeling with Python

Build the mathematical foundation behind modern machine learning and intelligent systems.

Linear Algebra for Intelligent Systems develops the core mathematical structures that power data science, artificial intelligence, and computational modeling.

Concepts are introduced geometrically, formalized rigorously, and reinforced with worked examples and implementation exercises in Python. The result is a clear path from abstract theory to applied systems.

Topics include:

• Vectors, norms, inner products, orthogonality, and projections

• Matrix operations, rank, determinants, and invertibility

• Systems of linear equations and matrix factorizations

• Vector spaces, basis theory, and rank–nullity

• Linear transformations and change of basis

• Eigenvalues, eigenvectors, and principal component analysis

• Singular value decomposition and low-rank approximation

• Gradients, Jacobians, Hessians, and matrix calculus

• Optimization methods and backpropagation

• Probability, covariance, and multivariate models

Designed for serious students, engineers, and researchers, this book connects rigorous linear algebra with the mechanics of modern learning systems. Linear algebra is not just preparation for intelligent systems—it is the language they operate in.