Cut the Crap Linear Algebra - Nico Biagio Ball

Have you ever read a book and thought, "Goodness gracious, I have no idea what the heck this guy is saying." So have I, and I have decided to counter such an ugly world of incomprehensible math with one that is made to be learned. Books of mathematics are far too concerned with impressing colleagues and hiding their incapabilities behind textbook definitions and assumptions of knowledge. I believe that math is made to teach. So I promise you there will be a definitional or grammatical error in this book, but I also promise you that you will learn more than you ever have in your life. Welcome to the world of Linear Algebra!

Chapter 1: Vectors- The Basics of Vectors- Basic Vector Operations- Polar Form of Vectors- The Dot Product- Orthogonality- Vector Norms>Chapter 2: Matrices- Systems of Equations- The Matrix- Matrix Operations- Determinants- The Cross Product- Inverse Matrices- Cramer's Rule and the Method of Inverses>Chapter 3: Linear Theory- Basic Pure Mathematics- Vector Spaces- Subspaces- Linear Independence- Span- Basis>Chapter 4: Eigenvectors and Diagonalization- Eigenvectors and Eigenvalues- Eigenspaces- Diagonalization>Chapter 5: Applications of Linear Algebra- The Gram-Schmidt Process- Least Squares Approximation- The Jacobian- Quantum Mechanics