Linear Algebra on the Subject GRE

GRE Math Subject · Axiom Academy

INTRO Linear Algebra on the Subject GRE Master the vector spaces, transformations, and eigenvalues that dominate the exam The GRE Subject Test devotes nearly 30% of problems to linear algebra. This unit covers everything you need to ace those questions. This 17-module unit takes you from foundational concepts to advanced problem-solving: Vector Spaces & Subspaces — bases, dimension, linear independence Linear Transformations — matrix representations, composition, kernels Determinants — computation, properties, geometric interpretation Eigenvalues & Eigenvectors — characteristic polynomials, diagonalization Inner Products — orthogonality, projections, Gram-Schmidt process Rank-Nullity Theorem — fundamental subspaces, rank calculations Core Lessons (6 modules): Rigorous definitions and theorems with worked examples Advanced Topics (2 modules): Inner products, rank-nullity, Jordan normal form Subject GRE Examples (4 modules): Authentic 5-choice problems from past exams with step-by-step solutions Interactive Drill: Matrix operations practice without a calculator — essential for speed Practice & Assessment: 8 practice problems + 15-question formal quiz Reference Materials: Formula sheet and summary for last-minute review Pro Tips for Linear Algebra Success The next module starts with vector spaces — the foundation of everything in linear algebra. You'll learn formal definitions, examples, and how to determine if a set is a vector space.

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