Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and engineering areas, because it allows modeling many natural phenomena, and efficiently computing with such models.

This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill.

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00:03:38​ Solving Systems of Linear Equation
00:14:55​ Using Matrices to solve Linear Equations
00:28:28​ Reduced Row Echelon form
00:37:08​ Gaussian Elimination
00:47:47​ Existence and Uniqueness of Solutions
01:02:18​ Linear Equations setup
01:09:31​ Matrix Addition and Scalar Multiplication
01:19:13​ Matrix Multiplication
01:31:28​ Properties of Matrix Multiplication
01:38:58​ Interpretation of matrix Multiplication
01:50:35​ Introduction to Vectors
02:02:30​ Solving Vector Equations
02:15:59​ Solving Matrix Equations
02:24:20​ Matrix Inverses
02:33:14​ Matrix Inverses for 2*2 Matrics
02:38:30​ Equivalent Conditions for a Matrix to be INvertible
02:45:34​ Properties of Matrix INverses
02:56:06​ Transpose
03:04:43​ Symmetric and Skew-symmetric Matrices

03:13:54​ Trace
03:23:01​ The Determent of a Matrix
03:35:17​ Determinant and Elementary Row Operations
03:47:28​ Determinant Properties
03:58:54​ Invertible Matrices and Their Determinants…
04:04:23​ Eigenvalues and Eigenvectors
04:20:55​ Properties of Eigenvalues
04:32:03​ Diagonalizing Matrices
04:45:16​ Dot Product (linear Algebra )
04:49:41​ Unit Vectors

04:54:41​ Orthogonal Vectors
04:59:27​ Orthogonal Matrices
05:07:06​ Symmetric Matrices and Eigenvectors and Eigenvalues
05:12:05​ Symmetric Matrices and Eigenvectors and Eigenvalues
05:18:17​ Diagonalizing Symmetric Matrices
05:29:17​ Linearly Independent Vectors
05:36:44​ Gram-Schmidt Orthogonalization
05:49:43​ Singular Value Decomposition Introduction
05:55:46​ Singular Value Decomposition How to Find It
06:11:16​ Singular Value Decomposition Why it Works

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