Linear Algebra
95 videos • 59,460 views • by Wrath of Math
A series of lessons on Linear Algebra. Consider joining the channel as a member to get access to the lecture notes, and exclusive and early videos! Textbook: Elementary Linear Algebra by Howard Anton
1
Row Echelon Form of the Matrix Explained | Linear Algebra
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2
Reduced Row Echelon Form of the Matrix Explained | Linear Algebra
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3
A Guide to Gaussian Elimination Method (and Solving Systems of Equations) | Linear Algebra
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4
Guide to Gauss-Jordan Elimination (and Solving Systems of Equations) | Linear Algebra
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5
Homogenous Linear Systems, Trivial and Nontrivial Solutions | Linear Algebra
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6
Find Pivots, Pivot Rows, and Pivot Columns with Row Echelon Form | Linear Algebra
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7
Transpose of a Matrix | Linear Algebra
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8
Trace of a Matrix | Linear Algebra
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9
Proof: Inverse of a Matrix is Unique | Linear Algebra
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10
Finding the Inverse of a 2x2 Matrix | Linear Algebra
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11
Inverse of a Transpose Matrix | Linear Algebra
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12
What are Elementary Matrices? | Linear Algebra
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13
Inverse Matrix by Gauss-Jordan Elimination | Linear Algebra
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14
Determine if Linear System is Consistent with Gaussian Elimination | Linear Algebra
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15
Diagonally Dominant Matrices - Invertible at a Glance! | Linear Algebra
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16
Solve Linear System with Inverse Matrix | Linear Algebra
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17
Solve Two Systems with Common Coefficient Matrix (Gauss-Jordan) | Linear Algebra
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18
Invertible Matrix Product has Invertible Factors | Linear Algebra
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19
Diagonal Matrices and their Properties | Linear Algebra
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20
Symmetric Matrices and their Properties | Linear Algebra
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21
Matrix Transformations and Linear Transformations | Linear Algebra
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22
Reflections as Matrix Transformations | Linear Algebra
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23
Find Standard Matrix from Vector Images | Linear Algebra
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24
Composition of Matrix Transformations | Linear Algebra
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25
Composition of Three Matrix Transformations | Linear Algebra
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26
Minors and Cofactors of a Matrix | Linear Algebra
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27
The Cofactor Definition of Determinants (Laplace Expansion Explained) | Linear Algebra
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28
Determinants of Triangular Matrices | Linear Algebra
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29
Diagonal Trick for Easy 3x3 Matrix Determinants! | Linear Algebra
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30
How Row Operations Change the Determinant | Linear Algebra
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31
Find Determinants with Row Reduction | Linear Algebra
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32
Properties of Determinants of Matrices | Linear Algebra
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33
Cramer's Rule for Solving System of Linear Equations | Linear Algebra
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34
Using Matrices for Cryptography | Linear Algebra
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35
How to Write a Vector as a Linear Combination of Vectors in R^n | Linear Algebra
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36
Orthogonal Vectors in R^n | Linear Algebra
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37
Orthogonal Projection of Vectors | Linear Algebra
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38
Vector Spaces Explained | Linear Algebra
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39
Vector Subspaces and Subspace Test Explained | Linear Algebra
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40
Spanning Sets in Vector Spaces | Linear Algebra
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41
Linear Independence in Vector Spaces | Linear Algebra
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42
Linearly Independent Polynomials | Linear Algebra
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43
Linear Independence of Functions with Wronskian | Linear Algebra
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44
Determine if a Set of Vectors is Linearly Independent | Linear Algebra Exercises
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45
Coordinate Vectors Relative to a Basis | Linear Algebra
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46
Dimension of a Vector Space | Linear Algebra
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47
Basis of Vector Space by Inspection | Linear Algebra
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48
Row Vectors and Column Vectors | Linear Algebra
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49
Column Space of a Matrix Explained | Linear Algebra
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50
Finding Basis for the Row Space of a Matrix | Linear Algebra
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51
Finding Basis for the Column Space of a Matrix | Linear Algebra
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52
Find Null Space and Nullity of a Matrix | Linear Algebra
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53
How to Find the Rank of a Matrix (with echelon form) | Linear Algebra
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54
The Four Fundamental Subspaces and the Fundamental Theorem | Linear Algebra
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55
Eigenvectors and Eigenvalues of a Matrix | Linear Algebra
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56
Eigenvalues of a Triangular Matrix | Linear Algebra
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57
Eigenspaces and their Bases | Linear Algebra
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58
Similar Matrices and Similarity Invariants | Linear Algebra
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59
Diagonalizing Matrices and Diagonalizability | Linear Algebra
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60
Powers of a Matrix with Diagonalization | Linear Algebra
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61
Algebraic and Geometric Multiplicity of Eigenvalues | Linear Algebra
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62
The Complex Dot Product (Euclidean Inner Product) | Linear Algebra
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63
Complex Eigenvalues Occur in Conjugate Pairs | Linear Algebra
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64
Characteristic Equations and Eigenvalues of any 2x2 Matrix | Linear Algebra
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65
Real Symmetric Matrices Have Real Eigenvalues | Linear Algebra
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66
Inner Products and Inner Product Spaces | Linear Algebra
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67
Angles and Orthogonality in Inner Product Spaces | Linear Algebra
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68
Triangle Inequalities in Inner Product Spaces | Linear Algebra
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69
Generalized Pythagorean Theorem in Inner Product Spaces | Linear Algebra
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70
Orthogonal Complements in Inner Product Spaces | Linear Algebra
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71
Orthogonal and Orthonormal Sets in Inner Product Spaces | Linear Algebra
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72
Orthogonal and Orthonormal Bases | Linear Algebra
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73
Orthogonal Projections on Inner Product Subspaces | Linear Algebra
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74
Gram-Schmidt Orthogonalization (Proof and Example) | Linear Algebra
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75
Least Squares Solutions and Deriving the Normal Equation | Linear Algebra
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76
Least Squares Fit of a Polynomial | Linear Algebra
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77
Orthogonal Matrices and their Properties | Linear Algebra
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78
Transition Matrix for Axes Rotation in 3D and 2D | Linear Algebra
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79
Orthogonal Diagonalization Explained | Linear Algebra
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80
Quadratic Forms in Matrix Notation | Linear Algebra
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81
General Linear Transformations on Vector Spaces | Linear Algebra
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82
Linear Transformations with Calculus | Linear Algebra
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83
Kernel and Range of Linear Transformations | Linear Algebra
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84
Rank and Nullity of Linear Transformations | Linear Algebra
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85
One-to-One and Onto Linear Transformations | Linear Algebra
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86
Inverse Linear Transformations | Linear Algebra
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87
Composition of Linear Transformations | Linear Algebra
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88
Isomorphic Vector Spaces and Isomorphisms | Linear Algebra
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89
Isomorphic Inner Product Spaces | Linear Algebra
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90
Matrices for General Linear Transformations | Linear Algebra
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91
Similar Linear Operators with Different Bases | Linear Algebra
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92
LU-Decomposition of a Matrix Explained | Linear Algebra
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93
LDU-Decomposition of a Matrix Explained | Linear Algebra
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94
PLU-Decomposition of a Matrix Explained | Linear Algebra
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95
Power Method for Dominant Eigenvalues and Eigenvectors | Linear Algebra
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