Overview

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Dive into a comprehensive 14-hour course on Linear Algebra, covering fundamental concepts and advanced topics. Begin with elementary linear algebra and matrix operations, including addition, subtraction, multiplication, and transposition. Learn about Gauss elimination, row-echelon forms, and Gauss-Jordan elimination for solving systems of equations. Explore matrix inverses, determinants, and eigenvalues. Study vectors, including dot products, cross products, and orthogonal projections. Delve into plane geometry and equations of planes. Examine vectors in n-dimensional space and Euclidean geometry. Conclude with an introduction to complex numbers, their operations, and polar form representations. Master essential linear algebra skills through numerous examples and problem-solving exercises throughout the course.

Syllabus

1 Elementary Linear Algebra.flv.
2 Construction of a Matrix-YouTube sharing.mov.
3A Matrix Addition and Subtraction-YouTube sharing.mov.
3B Addition and Subtraction Examples-YouTube sharing.mov.
4A Matrix Multiplication-YouTube sharing.mov.
4B Transpose of a Matrix-YouTube sharing.mov.
4C Properties of the Transpose.
5A Properties of Matrix Arithmetic-YouTube sharing.mov.
5B Commutative Law of Matrix Multiplication-YouTube sharing.mov.
6A Matrix Reduction with Gauss Elimination-YouTube sharing.mov.
6B Row-Echelon Forms-YouTube sharing.mov.
6C Reduced Row-Echelon Form with Gauss-Jordan Elimination-YouTube sharing.mov.
7A_1 Linear Algebra Definitons.
7A_2 Linear Algebra Definitions.
7A_3 Linear Algebra Definitions.
7B Inverse of a Matrix-YouTube sharing.mov.
7C Inverse of a Matrix Example 1-YouTube sharing.mov.
7C Inverse of a Matrix Example 2-YouTube sharing.mov.
7C Inverse of a Matrix Example 3-YouTube sharing.mov.
7C Inverse of a Matrix Example 4-YouTube sharing.mov.
7D Matrix Exponents.
7E The Elementary Matrix.
7F Diagonal Triangular Symmetric Matrices.
8 Row and Column Views of a Matrix.
9A_1 The Inverse of a Matrix.
9A_2 The Inverse of a Matrix Using the Idenity Matrix.
9A_3 The Inverse of a Matrix Using the Identity Matrix.
9A_4 The Inverse of a Matrix Using the Determinant.
9A_5 The Inverse of a Matrix Cramer Method.
9B The Determinant.
9C The Determinant.
9D The Determinant.
9E The Determinant.
9F The Determinant.
9G The Determinant.
9H The Determinant.
10A An Introduction to Eigenvalues and Eigenvectors.
11A Introduction to Vectors.
11B Introduction to Vectors.
11C The Norm of a Vector.
11D The Norm of a Vector.
11E The Dot Product.
11F The Dot Product.
11G The Dot Product.
11H Orthogonal Projection of a Vector.
11I Orthogonal Projection of a Vector.
11J Orthogonal Projection of a Vector.
11K More Example of Dot Product and Orthogonal Projections.
11L More Example of Dot Product and Orthogonal Projections.
11M The Cross Product.
11N The Cross Product.
11O The Cross Product.
11P The Cross Product.
11Q The Cross Product.
11R The Cross Product.
11S The Cross Product.
12A Equations of a Plane.
12B Plane Geometry.
12C Plane Geometry.
12D Plane Geometry.
12E Plane Geometry.
12F Plane Geometry.
12G Plane Geometry.
12H Plane Geometry.
12I Plane Geometry.
12J Plane Geometry.
12K Additional Plane Geomtery Facts.flv.
12L Additional Plane Geometry Facts.flv.
12M Additional Plane Geometry Facts.
13A Vectors in n Space.
13B Vectors in n Space.
13C Norm and Distance in Euclidean n Space.
13D Orthogonality.
13E A Matrix Equation for the Dot Product.
13F Example Problems for Euclidean n Space.
14A Introduction to Complex Numbers.
14B Complex Number Multiplication.
14C Matrices with Complex Number Elements.
14D Sample Problems.
14E Division of Complex Numbers.
14F Division of Complex Numbers.
14G Division of Complex Numbers.
14H Division of Complex Numbers.
14I Division of Complex Numbers.
14J Polar Form of Complex Numbers and the nth Root.
14K Polar Form of Complex Numbers and the nth Root.
14L Polar Form of Complex Numbers and the nth Root.
14M Polar Form of Complex Numbers and the nth Root.
14N Polar Form of Complex Numbers and the nth Root.
14O The nth Root of a Number.
14P The nth Root of a Number.
14Q The nth Root of a Number.