Hefferon's Linear Algebra (Fourth Edition)
by Jim Hefferon
Free proof-oriented undergraduate text whose entire Chapter Three, 'Maps Between Spaces', is devoted to linear maps: isomorphisms first, then homomorphisms, range space and null space, matrix representation, and change of basis. Full worked answers to every exercise.
More resources on Linear Transformations
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.
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.
Linear Algebra (MIT 18.06)
Matrix theory and linear algebra: systems of equations, elimination, vector spaces and subspaces, orthogonality and least squares, determinants, eigenvalues and positive definite matrices. Includes 35 lecture videos plus problem sets and exams with solutions, giving the fluency needed for applied mathematics, engineering and data science.
Vectors | Chapter 1, Essence of Linear Algebra
Opening chapter of Grant Sanderson's animated linear algebra series, contrasting the physics, computer science and mathematics views of vectors. Shows vectors as arrows and coordinate lists, and how addition and scalar multiplication work geometrically, laying intuition for linear combinations and transformations.
Interactive Linear Algebra — Chapter 3: Linear Transformations and Matrix Algebra
Georgia Tech's Math 1553 text, with draggable WebGL demonstrations. Chapter 3 works through matrix transformations, one-to-one and onto maps, the proof that every linear transformation is a matrix transformation, composition, inverses, and the Invertible Matrix Theorem.