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.
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.
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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