Linear Algebra Done Right
by Sheldon Axler · Sheldon Axler
Axler's widely used linear algebra textbook develops the subject through vector spaces and linear operators, deferring determinants until near the end. Covers eigenvalues, inner product spaces, and the spectral theorem, building conceptual understanding valued in later coursework in analysis, physics, and algebra.
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More resources on Vector Spaces
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Linear transformations and matrices | Essence of linear algebra, chapter 3
3Blue1Brown video explaining how matrices encode linear transformations of vector spaces, showing how basis vectors determine a transformation and how matrix multiplication corresponds to composing transformations. Part of the Essence of Linear Algebra series.
Linear Algebra - Khan Academy
Learn linear algebra fundamentals, including matrices, vectors, and transformations, with Khan Academy's comprehensive course.
Essence of Linear Algebra
Grasp determinants with 3Blue1Brown's "Essence of Linear Algebra" course. Visualize and understand this key linear algebra concept.
Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra
Chapter 2 of 3Blue1Brown's Essence of Linear Algebra series, a short animated lesson on linear combinations, span and basis vectors in 2D and 3D. Viewers learn to picture which points a set of vectors can reach and what linear dependence means geometrically.
Vector Spaces on nLab
nLab reference article defining vector spaces as modules over a field and framing them within category theory via the category Vect_k of vector spaces and linear maps. Useful for readers wanting the categorical view of linear algebra.