Linear Algebra

Dive into a comprehensive 7-hour course on Linear Algebra, covering essential topics from prelinear algebra to eigenvalues and eigenvectors. Master fundamental concepts such as Gauss-Jordan Elimination, matrix multiplication, vector operations, and subspaces. Explore advanced topics including linear transformations, determinants, orthogonal complements, and the Gram-Schmidt process. Learn practical applications like solving systems of equations, finding areas using determinants, and applying the least squares method. Develop a strong foundation in linear algebra through a structured curriculum that progresses from basic principles to complex mathematical concepts, preparing you for advanced studies in mathematics, engineering, and related fields.

Syllabus

Prelinear Algebra.
Linear Algebra.
Linear Algebra 2 : Gauss Jordan Elimination.
Linear Algebra 3 : Finding Number of Solutions.
Linear Algebra 4 : Multiplying Matrices.
Linear Algebra 5 : Elimination Matrix & Vectors.
Linear Algebra 6 : Vectors & Spans.
Linear Algebra 7 : Subspaces.
Linear Algebra 8 : Basis & Cauchy Schwarz Inequality.
Linear Algebra 9 : Plane Equations & Vector Triangle Inequality.
Linear Algebra 10 : Cross Product.
Linear Algebra 11: Null Space.
Linear Algebra 12 : Solving Ax = b.
Linear Algebra 13 : Linear Transformations.
Linear Algebra 14 : Magic Transformations.
Linear Algebra 15 : Rotate & Scale Vectors.
Linear Algebra 16 : Linear Transformation Projections.
Linear Algebra 17 : Determinants.
Linear Algebra 18 : Determinants & Systems of Equations.
Linear Algebra 19 : Find Area with Determinants.
Linear Algebra 20 : Transpose.
Linear Algebra 21 : 4 Fundamental Subspaces.
Linear Algebra 22 : Orthogonal Complements.
Linear Algebra 23 : Projections on Any Subspace.
Linear Algebra 24 : Least Squares Method.
Linear Algebra 25 : Change of Basis Matrix.
Linear Algebra 26 : Orthonormal Basis.
Linear Algebra 27 : Gram-Schmidt Process.
Linear Algebra 28 : Eigenvalues and Eigenvectors.
Linear Algebra 29 : Final Video.