ADVANCED LINEAR ALGEBRA Proofs, Geometry, and Applications: Inner Product Spaces - Spectral Theory - SVD - Quadratic Forms

By Mir Hossain

dvanced Linear Algebra: Proofs, Geometry, and Applications is a rigorous, student-friendly guide for learners ready to move beyond introductory matrix algebra and into the deeper structure of modern linear algebra.

Designed for upper-level undergraduates, beginning graduate students, and motivated self-learners, this book builds both proof skills and computational understanding across the most important topics in advanced linear algebra. Instead of presenting formulas in isolation, it connects algebraic ideas to geometry, intuition, and real applications.

Inside this book, you'll learn how to work with:

Vector spaces, subspaces, bases, and dimension

Linear transformations and matrix representations

Eigenvalues, eigenvectors, diagonalization, and Jordan form

Inner product spaces, orthogonality, and Gram-Schmidt

Spectral theorem and quadratic forms

Singular Value Decomposition (SVD)

Proof-based reasoning and theorem-driven problem solving

Applications to geometry, data methods, and scientific computing

This text is especially helpful for students transitioning from computational courses to proof-based mathematics, with clear explanations, structured examples, and practice that strengthens mathematical maturity.

Whether you are preparing for exams, supporting a university course, or building a stronger foundation for machine learning, optimization, physics, or applied mathematics, Advanced Linear Algebra provides the depth and clarity you need.

• Format: Paperback
• Language: English
• ISBN: B0GR9XVN7P
• ISBN13: 9798250818988
• Release Date: March 2026
• Publisher: Independently Published
• Length: 102 Pages
• Weight: 0.44 lbs.
• Dimensions: 0.3" x 6.0" x 9.0"