Linear Algebra/Print version/Part 2

__NOTOC__ __NOEDITSECTION__ Linear Algebra Chapter III - Maps Between Spaces Section I - Isomorphisms 1 - Definition and Examples 2 - Dimension Characterizes Isomorphism Section II - Homomorphisms 1 - Definition 2 - Rangespace and Nullspace Section III - Computing Linear Maps 1 - Representing Linear Maps with Matrices 2 - Any Matrix Represents a Linear Map Section IV - Matrix Operations 1 - Sums and Scalar Products 2 - Matrix Multiplication 3 - Mechanics of Matrix Multiplication 4 - Inverses Section V - Change of Basis 1 - Changing Representations of Vectors 2 - Changing Map Representations Section VI - Projection 1 - Orthogonal Projection Onto a Line 2 - Gram-Schmidt Orthogonalization 3 - Projection Onto a Subspace Topic: Line of Best Fit Topic: Geometry of Linear Maps Topic: Markov Chains Topic: Orthonormal Matrices Chapter IV - Determinants Section I - Definition 1 - Exploration 2 - Properties of Determinants 3 - The Permutation Expansion 4 - Determinants Exist Section II - Geometry of Determinants 1 - Determinants as Size Functions Section III - Other Formulas for Determinants 1 - Laplace's Expansion Topic: Cramer's Rule Topic: Speed of Calculating Determinants Topic: Projective Geometry Chapter V - Similarity Section I - Linear Algebra/Complex Vector Spaces 1 - Factoring and Complex Numbers: A Review 2 - Complex Representations Section II - Similarity 1 - Definition and Examples 2 - Diagonalizability 3 - Eigenvalues and Eigenvectors Section III - Nilpotence 1 - Self-Composition 2 - Strings Section IV - Jordan Form 1 - Polynomials of Maps and Matrices 2 - Jordan Canonical Form Topic: Geometry of Eigenvalues Topic: The Method of Powers Topic: Stable Populations Topic: Linear Recurrences Appendix Propositions Quantifiers Techniques of Proof Sets, Functions, Relations Resources And Licensing Bibliography Index