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# Linear Algebra

### Overview

This course on Linear Algebra aims to teach students the fundamentals of matrices, vector spaces, eigenvalues, and eigenvectors. By the end of the course, students will be able to manipulate matrices, evaluate determinants, understand vector spaces, perform linear transformations, and find eigenvalues and eigenvectors. The teaching method includes lectures, examples, and problem-solving sessions. This course is intended for learners who have a basic understanding of calculus and are looking to delve into the more abstract and applied aspects of mathematics.

### Syllabus

Introduction to Linear Algebra: Systems of Linear Equations.
Understanding Matrices and Matrix Notation.
Manipulating Matrices: Elementary Row Operations and Gauss-Jordan Elimination.
Types of Matrices and Matrix Addition.
Matrix Multiplication and Associated Properties.
Evaluating the Determinant of a Matrix.
The Vector Cross Product.
Inverse Matrices and Their Properties.
Solving Systems Using Cramer's Rule.
Understanding Vector Spaces.
Subspaces and Span.
Linear Independence.
Basis and Dimension.
Change of Basis.
Linear Transformations on Vector Spaces.
Image and Kernel.
Orthogonality and Orthonormality.
The Gram-Schmidt Process.
Finding Eigenvalues and Eigenvectors.
Diagonalization.
Complex, Hermitian, and Unitary Matrices.

### Taught by

Professor Dave Explains

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