Linear Algebra - Full College Course

Overview

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Dive into a comprehensive 12-hour college-level course on Linear Algebra taught by Dr. Jim Hefferon, professor of mathematics at St Michael's College. Explore fundamental concepts including solving linear systems, vector spaces, linear independence, basis and dimension, isomorphism, homomorphism, matrix operations, and more. Access the free accompanying textbook and additional resources to enhance your learning experience. Benefit from a structured curriculum covering topics from basic linear systems to advanced concepts like eigenvalues and eigenvectors. Supplement your studies with recommended learning resources and video series. Perfect for students seeking a thorough understanding of Linear Algebra principles and their applications in mathematics and related fields.

Syllabus

Introduction to Linear Algebra by Hefferon.
One.I.1 Solving Linear Systems, Part One.
One.I.1 Solving Linear Systems, Part Two.
One.I.2 Describing Solution Sets, Part One.
One.I.2 Describing Solution Sets, Part Two.
One.I.3 General = Particular + Homogeneous.
One.II.1 Vectors in Space.
One.II.2 Vector Length and Angle Measure.
One.III.1 Gauss-Jordan Elimination.
One.III.2 The Linear Combination Lemma.
Two.I.1 Vector Spaces, Part One.
Two.I.1 Vector Spaces, Part Two.
Two.I.2 Subspaces, Part One.
Two.I.2 Subspaces, Part Two.
Two.II.1 Linear Independence, Part One.
Two.II.1 Linear Independence, Part Two.
Two.III.1 Basis, Part One.
Two.III.1 Basis, Part Two.
Two.III.2 Dimension.
Two.III.3 Vector Spaces and Linear Systems.
Three.I.1 Isomorphism, Part One.
Three.I.1 Isomorphism, Part Two.
Three.I.2 Dimension Characterizes Isomorphism.
Three.II.1 Homomorphism, Part One.
Three.II.1 Homomorphism, Part Two.
Three.II.2 Range Space and Null Space, Part One.
Three.II.2 Range Space and Null Space, Part Two..
Three.II Extra Transformations of the Plane.
Three.III.1 Representing Linear Maps, Part One..
Three.III.1 Representing Linear Maps, Part Two.
Three.III.2 Any Matrix Represents a Linear Map.
Three.IV.1 Sums and Scalar Products of Matrices.
Three.IV.2 Matrix Multiplication, Part One.
Three.IV.2 Matrix Multiplication, Part Two.